It all makes sense now. Seriously, I felt so bad in my Calculus class because math used to be my favorite subject but my teacher sucks so none of us get any of what he says. YOU SIR, are perfect in every way. THANK YOU.
I actually really appreciate that he has trouble with the long division and stuff like that. Love the little side comments too "I haven't eaten dinner yet" LOL. Too funny... I wish you were my calc/physics teacher!
instead of x(24-2x)(24-2x), use your algebra with x(24-2x)^2, use the product rule when finding the derivative and you get 24-2x(24-6x), find your 0's on both sides. So much faster
I didn't mean to be rude, I just thought that it doesn't make sense to use advance technology such as this cyber-blackboard and opt to not use a calculator. Sal, your a big help. Thanks!
I really enjoyed these videos. I aced my calculus class, thanks for the help! BUT, my only qualm is that you have the title listed as calculus 2 optimization....this is not a level calculus 2 problem
i love this, "I've made so many care less mistakes." *gets right answer* "jeez i should have know that, i can't believe that I couldn't do it in my head" All i know is that your are very helpful.
Such a big fan Mr. Khan but pls get with a calculator. Most of us watching and ready to learn usually have a calculator handy to go along with you. Anyone who isn't is probably just watching a movie then
I think you are blowing things out of proportion. Perhaps you deem yourself to be an idiot since you have replied with such vehement comments about my intellectual capacity. Don't take things so personally.
Hey, how funny, your name is the same as my brother. I thought he will be the first and also the last has Sal for name, he he. BTW, thanks so much for the vids
You're using x to represent a length, so the initial interval you're dealing with should be something like [0,12] because you can't have a negative length, which means it should never be negative, but i don't see where the 8 is coming from. But, the idea is that you should watch the initial interval you can work with in the problem.
I would assume you've gone through the same pain as the students you are teaching, but for time conservation purposes maybe doing them ahead of time would be a good idea. But thanks for your work!
what advantage does taking the second derivative to find the maxima/minima have over creating a sign diagram for the first derivative? I tend to you the sign diagram because the second derivative laws seem too confusing.
Rather than take the second derivative to determine if it's a maximum, why not just plug 3 and 5 into V' for x? You will see that it is positive at 3, and negative at 5. If the equation goes from a positive to a negative at 4, than this would be a maximum on V.
only problem i have is that 24 inches squared is the area,and the way you drew it out it was 24x24 giving an area of 576 inches squared... at least thats how i see it
Yes but to save yourself some time use your TI-84 calculator (if you have one). Plug in the equation for Y1, then graph it. Then press 2nd, calc, #2 to find your zero. Saves a lot of time
thanks a lot and about the algebra it's okay dude we all make mistakes..thanks to silly mistakes i get the procedure right but not the answer..lol..anyway thanks a lot again
"i know its hard to read.. its hard to read for me" khan you are the coolest and best guy around
9:25 "Sometimes when your brain is in calculus mode, the algebra 2 gets difficult" My tests in a nutshell.
"I shouldn't have had to do that. I've made so many careless mistakes and I haven't eaten dinner yet"
lost it when you said that XD
Haha I know right!
"So many mistakes and I haven't even eaten dinner yet" Khan is the truth.
It all makes sense now. Seriously, I felt so bad in my Calculus class because math used to be my favorite subject but my teacher sucks so none of us get any of what he says. YOU SIR, are perfect in every way. THANK YOU.
Really appreciate your videos. The struggles you exhibit help us all feel human!
I love this dude he is so charismatic lol great explanation
we need more people like you on this planet...people who arent afraid to show what they're passionate about and care about what they do
My calculus exam is in two days. You are saving my life right now. THANK YOU.
"Sometimes when your brain is in calculus mode the algebra 2 gets difficult" lmaoooo this is so good
Thank you for letting me intuitively visualize these universal math concepts!!!
Fun drinking game: take a shot every time he says "this"
ArashkG
50 shots in this video
Afshar ali: The Great Iranian what made you want to count that?
I actually really appreciate that he has trouble with the long division and stuff like that. Love the little side comments too "I haven't eaten dinner yet" LOL. Too funny... I wish you were my calc/physics teacher!
YOU GO THROUGH THE SAME PAIN WE DO, I RESPECT YOU SIR
don't be so hard on yourself Hal, your a badass.... and no careless mistake is gonna change that
I just go home during calc and watch khan academy. Sal, you the man!
Thank you Sal for doing this! You make everything understandable.
You ought to consider being a radio DJ on your off time. You soothing voice demands such intelligence!
hardest part of these problems is the algebra.
It's so easy when explained clearly.. thanks.
I agree the hardest part to these questions is algebra. So caught up on calculus that I keep messing up on the simplest algebra.
If it says 24 in sq, shouldn't length be 12 inches?
Sgt. Keyboard Warrior Should be square root of 24 as length
love this guy!! He makes doing math so much more fun!!!
instead of x(24-2x)(24-2x), use your algebra with x(24-2x)^2, use the product rule when finding the derivative and you get 24-2x(24-6x), find your 0's on both sides. So much faster
If you already know why watch this video?
@@mosesfuego7086 To help other people who might not know this?
Thanks to this, I passed my Calculus test :D
glad to know you're actually a human and have to write out some math, great video! thanks!
You're a credit to the field of YouTutors!
khan academy do be saving lives
I didn't mean to be rude, I just thought that it doesn't make sense to use advance technology such as this cyber-blackboard and opt to not use a calculator.
Sal, your a big help. Thanks!
U are an awesome teacher
Thanks a lot! Saved me from a headache
Good to see Sal checking if he makes mistakes and forgetting simple division/multiplications, shows us that everyone makes brain fart moments!
You Sir, are my hero.
AMAZING!!! Thank you so much!
"its kinda sad" LOOL...you make calculus fun
Calc final tomorrow? Better watch all these videos tonight.
I really enjoyed these videos. I aced my calculus class, thanks for the help! BUT, my only qualm is that you have the title listed as calculus 2 optimization....this is not a level calculus 2 problem
i love this, "I've made so many care less mistakes."
*gets right answer*
"jeez i should have know that, i can't believe that I couldn't do it in my head"
All i know is that your are very helpful.
so much clearer now..thanx
told you Khan would help.
yea
when he was like i should have memorized my times tables up to 25 i was like O_O
that literally saved me from having to look at my indiscernible calc notes from class that I keep sleeping through...
@riku0228 no, they have to multiply to 48, 8*8 = 64
Optimization-calculus is so much fun.
Tq very much..i learned a lot from u
I have the same question in my textbook; so, 24 inches square isnt the total area? Rather, it is stating that each side length is 24?
Such a big fan Mr. Khan but pls get with a calculator. Most of us watching and ready to learn usually have a calculator handy to go along with you. Anyone who isn't is probably just watching a movie then
I actively watch all the videos without a calculator. It's called using your brain : )
Let me guess, you're an idiot? Maybe you should read in btwn the lines before commenting idiot.
Oh let me help u out since your brain couldn't process my points. Using calculator will help shorten the videos, idiot, got it?
I think you are blowing things out of proportion. Perhaps you deem yourself to be an idiot since you have replied with such vehement comments about my intellectual capacity. Don't take things so personally.
I'm on break now..I'd rather direct my energy to something else in lieu of replying an idiot's sarcasm
1:45
"S-sex"
Khan! There might be children watching! :O
What about a closed box? I can't find any examples anywhere.
It seems the difficult part is just find the main function
Hey, how funny, your name is the same as my brother. I thought he will be the first and also the last has Sal for name, he he. BTW, thanks so much for the vids
I really like the part where Sal did the math.
What if the question said that the box had to be a perfect cube with the 24×24 cardboard?
@lucasbudega it says calculus 2 because it is the second in a series of videos :)
@misscollegiate08 You're absolutely right. Bad day, sorry for any confusion.
Sal can you please do reimann sums? I know you have but so much time, but I'd really appreciate it.
"when your brain's in Calculus mode, sometimes the Algebra II gets hard!" (: haha. so true
what if the box is not open? will it be the same process? or is there a different vid?
you are my hero!
What do you use for you blackboard?
You're using x to represent a length, so the initial interval you're dealing with should be something like [0,12] because you can't have a negative length, which means it should never be negative, but i don't see where the 8 is coming from. But, the idea is that you should watch the initial interval you can work with in the problem.
i think if you cut squares ,u cant make a box since two sides of the box have to overlap the other two sides,unless u cut a rectangle
Is it Calculus 2 or the second video of optimization?
+Sofia Eff Fernando this is part 2
I would assume you've gone through the same pain as the students you are teaching, but for time conservation purposes maybe doing them ahead of time would be a good idea. But thanks for your work!
What do you use to write this all on?
what advantage does taking the second derivative to find the maxima/minima have over creating a sign diagram for the first derivative?
I tend to you the sign diagram because the second derivative laws seem too confusing.
Goutam Singh It just depends which way is faster
your voice is very good
hey how old are you are you a professor? or a student you seem smart
"I haven't eaten dinner yet." hahahaha
dude,...... thank you so much
Rather than take the second derivative to determine if it's a maximum, why not just plug 3 and 5 into V' for x? You will see that it is positive at 3, and negative at 5. If the equation goes from a positive to a negative at 4, than this would be a maximum on V.
The great Sal does not need a calculator :P
You draw a swiss cross and say "crux of the problem." Win.
thank you
he didnt mean that it was a calc 2 problem. He meant " optimization with calculus..Problem 2"...
his name is Sal god damn it.
Only people who watched rush hour 2 will understand.
only problem i have is that 24 inches squared is the area,and the way you drew it out it was 24x24 giving an area of 576 inches squared... at least thats how i see it
V'(x)=12x^2 -196x + octopus
you are saving my life :)
@SeekTheTruth7890 it's single variable calculus so probs.
"Sometimes when your brain is in calculus mode, algebra 2 gets difficult." Ohhh yeah.
Shouldn't the equation be Volume - empty square ((24-2x)•(24-2x))
theres is one thing that confuses me now... if x=0, then the volume should be equal to 48 according to the volume expression?! : /
my god, very good. very very good.
he is a legend!!!
It's actually Salman.
Just want to point out that "4" is not a volume. The final answer is (4x16x16)= 1024 in^3
Yes sure Sir. 4 is just the value of x.
9:00 could you use the quadratic formula to solve for zero?
Yes but to save yourself some time use your TI-84 calculator (if you have one). Plug in the equation for Y1, then graph it. Then press 2nd, calc, #2 to find your zero. Saves a lot of time
@@lexilikesbugs 👍
Why cant you be my calculus professor
why concave downwards? 4:00
because the second derivative is negative
Tell us how you did :)
like one time during calculus class, i forgot 2x3.
Learned trigonometry and how to stuff bacon in lussanya plz
thanks a lot and about the algebra it's okay dude we all make mistakes..thanks to silly mistakes i get the procedure right but not the answer..lol..anyway thanks a lot again
shortcut divide it by six you got the answer
squeezing 10 weeks worth of calculus lectures into 1 night
1st thing to do
KHANACADEMY !
dude..........thanks
you're so helpful =]
At the end you made a mistake, it is not "min." value, it is "max" value. Watch out next time! ;)
Paaa-llleeeeaaassssee be my math teacher!!
@klevn (24-2x)(24-2x) = 576-48x-48x+4x^2 = 576-96x+4x^2