INFLECTION POINTS and CONCAVITY (KristaKingMath)
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- Опубліковано 9 лют 2025
- ► My Applications of Derivatives course: www.kristaking...
Inflection points are points at which a function changes concavity, from concave up to concave down, or vice versa. To find inflection points, we'll need to find the second derivative of the original function, and then set it equal to 0 and solve for x. This will give us any possible inflection points of the function.
Once we have the potential inflection point(s), we can use the second derivative test to verify that the function is concave up on one side of the inflection point, and concave down on the other. If concavity is different on either side of the point, then we've confirmed that the point we found earlier is in fact an inflection point. Otherwise, if concavity is the same on either side of the point, then the point is not an inflection point.
Using this method we can also find all of the intervals on which the function is concave up, and all of the intervals where it is concave down.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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Your voice is so calming, it balances out the mildly panicky voice in my head
Also it's cool how you just get straight into working. Most people try to explain the abstract idea before any examples and that seems utterly backwards to me.
You'd be great at guided meditation, relaxation, ASMR, etc; one of the most placid voice I've heard.
you're a life saver, thank you so much for these videos, they are so simple and straight to the point. ❤️❤️
THANK YOU!!!!! You saved me I was having a breakdown because my textbook made no sense
You're welcome, I'm so glad this helped!!
Most concise video & explanation on YT.
Aw thanks! Glad you liked it.
Thank you so much, I highly appreciate this video. spot on.
Thanks! :)
Very well explained! I understood 100%!
+Jeffrey Chue That's awesome, I'm so glad it made sense!
you're really good at explaining ... also thanks for those helpful lessons
+7amad Mohammed AlDhanhani Thanks! Glad you like them.
+CalculusExpert.com ( could you please in the very soon future make & post integration or untiderivatives cuz we will be studing them )
Thanks again
such a nice teacher, thanks!
You're an amazing teacher, thank you
Thank you so much, I'm happy to help! :)
Mam, the way u explains was just awesome
Thank you! This video was very helpful :D
+Olivia Figueras Awesome! I'm so glad it helped!!
I like ur lectures
i understood all of it.. i have exam tomo nd i was so worried bout it thank u sooo much 💕
Oh good! I'm so glad it helped, and I hope your exam went great! :D
what to do if we have a rational inflection point value?
Thank you so much!
You're welcome! :)
Miss have you made any video covering the topic derivatives of higher degrees .It will be very helpful if you send me a link!
thanks help so muj..
New sub! So glad I found this vid
Thanks for subbing, Kristi!
thanks!
You're welcome Deven! :)
that was amazing
Just subbed and turned on notifications for your channel! Thanks for being such a great instructor! Where did you complete your college education and in what field?
Aw thanks! I'm glad you're liking the videos. :) I studied at the University of Notre Dame. I actually majored in Psychology, but tutored calculus during my time there.
F"(x) =+ means local min and if - then local maximun there
CD means convex
plz solve trigomometry inequality by this method
Why not check the next derivative and see if it's increasing or decreasing at the inflection point? f'''(-1) = 12 which means f''(x) is increasing at the inflection point, so the function f(x) goes from concave down to concave up.
FROM MOROCCO THANK YOU
tyyyy
You're welcome, Momtaz!! :)
HALLELUJAH
concave up = cup, concave down = frown
Why is that the other tutor ....takes the 0 into the right side like this 12×+12=0
Mistake at f(-1)...mam... I think the answer is -2, instead of 10.
Why do you say that? I still think f(-1)=10.
f(-1) = 2(-1)^3 + 6(-1)^2 - 5(-1) + 1 = -2 + 6 + 5 + 1 = 10
concave up.... smiling
concave down.... frowning.