This was so, so helpful! Not just because of your clear explanation, but because of your calm and understanding tone. I know it sounds dumb, but I felt less pressured to rush through concepts and was actually motivated to understand each step. Thank you!
Awww, that makes me so happy, Kayla! Math shouldn't be scary... we should just be able to hang out and work on it at our own pace, just tackling each little piece as we get to it. I want my videos to feel peaceful like that.
You just taught me this in roughly 5 minutes skipping over what I knew. I'm SITTING in my Calc class with my foreign teacher and haven't learned crap. Thank You
Another great video! One comment on optimization problems found in textbooks: Setting up the equation to optimize is sometimes the hardest part, and the books frequently do a poor job explaining the "setup". I ran across a Revenue optimization problem that was a little confusing as to where the p(x) (i.e. the specific equation that expressed p(x)) came from; But you've done a great job of setting everything up in this demo! Thank you again.
this would've been so helpful in calc 1 last semester... oh well! i'm glad other students will be able to benefit from your videos though, you explain these concepts very well. thank you for sharing your knowledge with the youtube community :)
if the y-value for both endpoints is equal, then you have to call both of them local maxima. only if there is just one point that is higher than any other can you call it a global maximum. hope that helps! :)
I found the applied example really helpful. For me it helps to see the equations "do something". Like watching a machine run helps you understand what its parts do, if that makes any sense.
I only plugged them in for x. Remember that the left-hand side of the equation is y(x), so when I plugged them in it looked like y(-2). On the right-hand side, I plugged them in wherever I had an x variable. Therefore, the result for each point was something like y=-1. Hope that helps! :)
This video really helped :) I was really confused in class when we were doing this, but now I actually get the concept of it and what to look for in the problem. But, like somebody else said, I think it would be a good idea to have text of the problem on the screen so that we can read it while your saying it, or even copy it down. Thanks for the help!
Thank you thank you THANK YOU for these videos! The thing that sucks about my calculus class is that it's near the end of the day, and I'm so exhausted by the time I get to that class, so it's almost impossible for me to pay attention (if only my school would sell iced coffee, or allow students to leave the school and come back, at least...) .I focus all of my energy in just trying to stay awake :( But these videos really save me!
Ian F Hi, She just factored out 4x from the parenthesis (aka Brackets in some countries). When She factored out the 4x, she had to divide 1/4x to 4x and 2916/x^2. When she divided the 1/4x to the expression, the values turned to 4x(1- 2916/4x^3). She then simplified the 2916/4 to 729 and thus she got 4x(1-729/x^3) Sorry if I used the wrong terms.
sorry about that! this was just a really broad overview video that wasn't intended to go into a lot of detail, but I have a lot more videos that are more in depth that i hope you'll check out! :D
I must say that I love your videos. They're always helpful. I used to be terrible at math but ended end going from pre algebra to calc in a year! You are living proof that beauty and brains can go together! (I already believed they could go together btw. Lol)
Very nice video. I love the instructor, too. You sound very nice and confident. One suggestion, though, it might help us visualize the problem if you present it in written form at the same time you're saying. I love your videos, though.
because the function as it's largest value in the interval at x=2. we want to know what the value is there, so that we can say "the global maximum is 11 at x=2". :)
You asked this 4 weeks ago so you might not care anymore or even remember making this comment, but she accidentally put in "6" instead of "0" for the second term (2x). So if you solved it as it looks, yes, it's 11. But if you solve it for f(0) then it would come out to be -1.
I think 22 people mistook the unlike button for the like button. You're amazing, so keep doing what you're doing~ Btw, do you have heterochromia? Cause your eyes look amazing! Love, a sophomore in high school ;)
my only problem is whenever the problems aren’t that simple. my teacher gave this problem Shakira is 5 miles off shore in a boat trying to escape a band of pirates! She wishes to reach a point on the coast 6 miles down shore where there is safety. She can row at 2 mph and walk at 4 mph. Where should she land the boat to reach down shore as quickly as possible I understand we are minimizing town but how tf am I supposed to know what the equation for time is when we never practice that. I’ve had an A all year and optimization is the only thing I don’t understand. My teacher makes it sound like common sense but that’s because she already knows how to solve it My teacher also said going straight down makes no sense so she didn’t solve for that but why doesn’t it if it’s twice as slow to row
i have basically this question (except there are no constraints on dimension) but the other constraint they put is that the box is 2cm cubic centimeters thick....where would i add in this 2cm into the equation? I agree with others and how setting up is usually the hardest part
I just factored out a 4x. When you pull 4 out of 2916 you get 729. And when you pull x out of 1/x^2, you have to put an x into the denominator to compensate for the one you pulled out, so you 1/x^3. I hope that helps!
The 2xh's are the ends of the box, so you include them. It's one of the 2x^2's that you leave out, since the box is topless. Notice from the diagram that the bottom is defined as 2x times x. :)
is it me or did she take the are wrong? A= 2( LB+BH+HL ) A= 2( 2x*x + x*h + h*2x) A= 2(2x^2 + xh + 2xh) A= 4x^2 + 6xh and she stated it A= 2x^2 + 6xh ?
This is an "open-top box", meaning that the top is missing, so you only include the bottom in the area, not the top and the bottom. That's why that extra area is missing from the formula. If the box were enclosed on all sides, you'd use the formula you have here. I hope that helps!
In calculating maxima and minima for y=x³+x²-x+1 I used 1 as the right endpoint and got 2 which is the same y value as critical point -1. How do you decide which is the local and which is the global maximum in a case like that?
Was it possible that at the end of the video the 9 was a local maximum? and if so, then what it would have mean since we are looking for the lowest value of x?
This was so, so helpful! Not just because of your clear explanation, but because of your calm and understanding tone. I know it sounds dumb, but I felt less pressured to rush through concepts and was actually motivated to understand each step. Thank you!
Awww, that makes me so happy, Kayla! Math shouldn't be scary... we should just be able to hang out and work on it at our own pace, just tackling each little piece as we get to it. I want my videos to feel peaceful like that.
jesus christ. Thanks so much for this. I understood more in 9 minutes than in 2 hours.
She looks like my 1year College Math Lecturer. Respect and thank you for you time Miss King.
People like you are saving Calculus grades 1 video at a time. Saves me a weeks worth of confusing lectures in ten minutes. Thank You!
You just taught me this in roughly 5 minutes skipping over what I knew. I'm SITTING in my Calc class with my foreign teacher and haven't learned crap. Thank You
Saving my Final score right now, thank you so much.
+Nick Koch You're welcome, I'm so glad it helped!
+CalculusExpert.com Let me know if you need a boyfriend :)
+Nick Koch Dude, "It feels good to be a gangster."
Smooth, too bad she never answered lol
Oh my GOODNESS! This was 2012 - 10 years ago. I THANK YOU SO MUCH FOR THIS!!!!
On [-2,2], the function attains its maximum value at x=2, i.e., f(2)=11 is the maximum value of the function on the closed interval [-2,2].
Another great video!
One comment on optimization problems found in textbooks:
Setting up the equation to optimize is sometimes the hardest part, and the books frequently do a poor job explaining the "setup". I ran across a Revenue optimization problem that was a little confusing as to where the p(x) (i.e. the specific equation that expressed p(x)) came from;
But you've done a great job of setting everything up in this demo!
Thank you again.
Thank you so much!
Saving time and confusion, that's a win win! :) Glad I could help!
you're welcome, that's awesome! i'm so glad it made sense! :D
this would've been so helpful in calc 1 last semester... oh well! i'm glad other students will be able to benefit from your videos though, you explain these concepts very well. thank you for sharing your knowledge with the youtube community :)
I'm mesmerized by your eyes. Instant love for mathematics.
You're welcome! Thanks for the comment. :)
Thank you, based math-lady.
You too! Thanks for the comment. :)
got a test tomorrow and your video just saved me... thanks!
if the y-value for both endpoints is equal, then you have to call both of them local maxima. only if there is just one point that is higher than any other can you call it a global maximum. hope that helps! :)
i would LOVE to move to New Zealand!! I've always wanted to visit! :) for now though, i hope the videos keep helping!! :D
you are better than my calc teacher! Be my teacher!! :)
got a test tomorrow on this, but I understand now! thanks!
Explanation of Calculus benefits those that truly know calculus, Thanks
I found the applied example really helpful. For me it helps to see the equations "do something". Like watching a machine run helps you understand what its parts do, if that makes any sense.
This was very helpful and made a lot more sense here than in class.
Each of those terms is the area of one side. For example, the width is x and the height is h, so the area of one side is xh. Hope that helps! :)
I only plugged them in for x. Remember that the left-hand side of the equation is y(x), so when I plugged them in it looked like y(-2). On the right-hand side, I plugged them in wherever I had an x variable. Therefore, the result for each point was something like y=-1. Hope that helps! :)
This was so helpful! I lost all of my calculus notes for this chapter and you have saved my life!!!😂
This video really helped :) I was really confused in class when we were doing this, but now I actually get the concept of it and what to look for in the problem. But, like somebody else said, I think it would be a good idea to have text of the problem on the screen so that we can read it while your saying it, or even copy it down.
Thanks for the help!
How do you go from 4x-2916/x^2 to 4x(1-729/x^3)
i was confused at this point too, but after looking closely, she had to factor out 4x to get [1 - (729/x^3)]
wow this was the best explanation ever
You were so good at explaining the concept and the process! You're really pretty too.
Thanks! These surface area ones always drive me nuts, but luckily you've saved me for my calc final in 7 hours lol
Thank you!
Oh, at 3:23 in the video Y prime of zero has a 2*6 but I believe it's 2*0. Just a friendly note. =)
Thanks for the good suggestion... I'm so glad you like the videos! :)
You're welcome! I'm so glad I can help! :)
Bummer! I wish I could have helped you earlier, but like you said, hopefully others will still benefit in some way. :)
Thank you thank you THANK YOU for these videos! The thing that sucks about my calculus class is that it's near the end of the day, and I'm so exhausted by the time I get to that class, so it's almost impossible for me to pay attention (if only my school would sell iced coffee, or allow students to leave the school and come back, at least...) .I focus all of my energy in just trying to stay awake :( But these videos really save me!
I'm so glad they've been helpful! Afternoon classes are the toughest!
Great explanation
Thanks!
fantastic video
however, not what you do to get from A'=4x-2916/x^2 to 4x(1-729/x^3)
8:02 into the video
Ian F Hi,
She just factored out 4x from the parenthesis (aka Brackets in some countries). When She factored out the 4x, she had to divide 1/4x to 4x and 2916/x^2. When she divided the 1/4x to the expression, the values turned to 4x(1- 2916/4x^3). She then simplified the 2916/4 to 729 and thus she got 4x(1-729/x^3)
Sorry if I used the wrong terms.
you're welcome, i'm glad it helped! and thanks for the feedback about the text of the question... that helps! :D
sorry about that! this was just a really broad overview video that wasn't intended to go into a lot of detail, but I have a lot more videos that are more in depth that i hope you'll check out! :D
this was complicated and messy .. you make it easy :) thank u
Glad I could help simplify it! :)
I must say that I love your videos. They're always helpful. I used to be terrible at math but ended end going from pre algebra to calc in a year!
You are living proof that beauty and brains can go together! (I already believed they could go together btw. Lol)
Thanks Ryan! And congrats on getting control of math, I'm so impressed with your improvement in such a short period of time! Keep up the good work! :D
ur amazing! passed my calc final bc of u thank uuu
this is what I have been looking for, thank
ua-cam.com/video/XQIbn27dOjE/v-deo.html 💐💐
Thank You Very Much!! the video helped me so much in preparation for my Electrical Engineering board exams this September 2016. :D
You're welcome, I'm glad I could help! Good luck on your exams this fall, I hope they go great!
thanks. I'll inform you if i pass the exams :D
That would be great, I'd love to hear how you do!
I don't have whats app, sorry about that!
Very nice video. I love the instructor, too. You sound very nice and confident. One suggestion, though, it might help us visualize the problem if you present it in written form at the same time you're saying. I love your videos, though.
Thank you so much for making this, i figured out related rates, but this just escaped me
So glad I could help! :)
I factored out a 4x. If you multiply 4x by the factor (1-729/x^3), the result will be the previous step. :)
because the function as it's largest value in the interval at x=2. we want to know what the value is there, so that we can say "the global maximum is 11 at x=2". :)
Very helpful video, it helped me fill in the the minor details. Thanks!
I'm so glad I can help!
You are a lifesaver! thanks!
Krista you're amazing !! Thank you !
Aw thanks! Glad I could help. :)
at 4:31 isn't the right endpoint y(1)?
The explanation is clear for me. Thank you so much!
You're welcome! Glad you liked it! :)
your method is very clear
i am in love with your videos😍😍😍😍
Good evening and thank you ma for delineating optimization to me.
Please don't stop making videos..
I am gonna check when I will start earning
On 3:54 how did you get -1 on yprime(0)? Isn't it 11?
You asked this 4 weeks ago so you might not care anymore or even remember making this comment, but she accidentally put in "6" instead of "0" for the second term (2x). So if you solved it as it looks, yes, it's 11. But if you solve it for f(0) then it would come out to be -1.
I want to say that you are a great teacher and beautiful as well!
(2916/x^2) == (2916x^-2). Factoring means you subtract from what you have. Take out a 4x and you have just what she said.
Glad you liked it!
You are right bro!!!!!!!!! she is amazing man!!!
This channel is spectacular! SO helpful!:)
Awww! That's awesome! Thank you!! :D
The world seems so easy to live in now! Thanks! :D
Hi! I'm sure this is a simple answer but I'm confused at 4:19 how you went from your right endpoint being 1 to then being 2? Why is that?
I have a lot of worked examples on my website. :)
ur just gorgeous !! plus u helped me a lot to be prepared for my test tomorrow.. Big thanx
Wooo last minute studying for calc final tomorrow
This the new wave, get a hottie, intelligent lady to explain maths on UA-cam. Profit.
dont be creepy
Awesome! Thanks for letting me know. :)
That was really interesting Krista :)
Awesome video! Thanks your help
You're welcome, Michael, I'm so glad it helped! :D
Thank you so much! You really helped me a lot.
I wish you were my calc teacher, maybe i'd actually learn something haha. thanks for the help!
I think 22 people mistook the unlike button for the like button.
You're amazing, so keep doing what you're doing~
Btw, do you have heterochromia? Cause your eyes look amazing!
Love, a sophomore in high school ;)
my only problem is whenever the problems aren’t that simple. my teacher gave this problem
Shakira is 5 miles off shore in a boat trying to escape a band of pirates! She wishes to reach a point on the coast 6 miles down shore where there is safety. She can row at 2 mph and walk at 4 mph. Where should she land the boat to reach down shore as quickly as possible
I understand we are minimizing town but how tf am I supposed to know what the equation for time is when we never practice that. I’ve had an A all year and optimization is the only thing I don’t understand. My teacher makes it sound like common sense but that’s because she already knows how to solve it
My teacher also said going straight down makes no sense so she didn’t solve for that but why doesn’t it if it’s twice as slow to row
Thanks to you I passed my calc class!!!!!!!! Just wanted to come back and say you're amazing, and damn cute. Thanks for everything girl
Awesome!
Thank you, you’re my favorite ✅✅✅✅✅
Awww, thanks Feza!
Feza Mto trujkpwads
i have basically this question (except there are no constraints on dimension) but the other constraint they put is that the box is 2cm cubic centimeters thick....where would i add in this 2cm into the equation? I agree with others and how setting up is usually the hardest part
in the first example did you plug in f(2) because it was a critical point?
That's so awesome! Thanks for the letting me know. :)
On 7:47, I dont understand how you got A' = 4x(1- 729/x^3).
I just factored out a 4x. When you pull 4 out of 2916 you get 729. And when you pull x out of 1/x^2, you have to put an x into the denominator to compensate for the one you pulled out, so you 1/x^3. I hope that helps!
Thank you very much for your help!
cool , you guys just saved my life
You're welcome!! :)
Thanks!
But, in the case of the surface area, wouldn't you neglect one of the 2xh's, given that the box is topless?
The 2xh's are the ends of the box, so you include them. It's one of the 2x^2's that you leave out, since the box is topless. Notice from the diagram that the bottom is defined as 2x times x. :)
Glad it helped. :D
is it me or did she take the are wrong?
A= 2( LB+BH+HL )
A= 2( 2x*x + x*h + h*2x)
A= 2(2x^2 + xh + 2xh)
A= 4x^2 + 6xh
and she stated it
A= 2x^2 + 6xh ?
This is an "open-top box", meaning that the top is missing, so you only include the bottom in the area, not the top and the bottom. That's why that extra area is missing from the formula. If the box were enclosed on all sides, you'd use the formula you have here. I hope that helps!
Thank you for this great video!!
you're welcome, i'm glad you liked it!! :D
Final on Thursday. Thanks for helping. :)
You're welcome! Good luck on the final!!
Also for the surface area of a box problem is there not another 2x^2? (2x^2+2x^2)
Ivan Castro No, because it's an open-top box (it has no top), so you don't include the surface area for that side.
integralCALC ohh thank you... rookie mistake.
so if it was NOT an open box. it would be 4x^2 at the end of the optimization equation correct?
yep! :)
In calculating maxima and minima for y=x³+x²-x+1 I used 1 as the right endpoint and got 2 which is the same y value as critical point -1. How do you decide which is the local and which is the global maximum in a case like that?
I hope you're able to get back in and take it! :)
Was it possible that at the end of the video the 9 was a local maximum? and if so, then what it would have mean since we are looking for the lowest value of x?
Hi, in the first example, for the right endpoint, I was unsure of why you plugged in 2.