How to find CRITICAL POINTS (KristaKingMath)

► My Applications of Derivatives course: www.kristaking...
The critical points of a function are the points at which the function changes direction from increasing to decreasing, or vice versa. Critical points are valuable because they will be the points at which the function has a local or global maximum, or a local or global minimum. In other words, the extrema of a function will always be located at critical points, so if we can find the critical points of a function, we'll also be able to find the function's extrema.
Luckily, to find critical points, all we have to do is take the first derivative of the function, set it equal to 0, and solve for x. This will give us any potential critical points. The tricky part is that the points we find with this method are only potential critical points. In order to prove that they are in fact critical points, we have to prove that the function changes direction at those points, which we'll do using the first derivative test.
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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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[@jenishere617]

Thank you for actually explaining why and not just showing us how to solve these problems. For some reason knowing why I’m doing something really cements the concepts better for me.

[@muhiebaljazzar4607]

!god are you a great teacher or what you can't imagine how desperate I was before I watched this lol

[@kristakingmath]

I'm so glad it could help! :)

[@jdcis2smart]

I can't reply to Earlyn's comment directly, so I'll just leave this right here. When you look for critical points, set the derivative of your function equal to 0. In this case, you will get y' = 4x^3 + 3x^2 + 6x. Factor your derivative and set both products equal to 0. Once you find the values of x that make your derivative equal 0, create a number line to check for the sign of the first derivative for all values to the left and right of your critical numbers (pick 1 number greater than your critical number and 1 number less than your critical number and plug them into your derivative). If there is a sign change, then you have found a critical point, but make sure you plug it into your original function to make sure that that critical point is defined.

[@user-wb2kp7cd9l]

Math Queen! Thx for your friendly explanation! You are really talented at teaching!

[@kristakingmath]

Thank you so much, Peto! :)

[@ColtonTrujillo]

I am not understanding why negative numbers are not in the domain of the original equation. I understand that the graph can demonstrate this, but can anybody tell me how you could know that negative numbers are not in the domain without actually graphing the original equation?

[@shaojunjia6654]

Krista King I love your explanations, they are concise and easy to follow. But I have a doubt. how is -2 not in the domain? I think the domain is all real number except x=0, There is a left-hand portion of this function, and -2 is the max on the interval (infinity, 0). Could you please double check? Thank for your clarifying.

[@eliashousseini9534]

Usually, only programming channels earn my sub, YOU ARE AN EXCEPTION :D

[@kristakingmath]

😀

[@Eric-sq5fs]

at 8:57 you have confused critical point with inflection point. Curvature is associated with the latter.

[@nathantonning]

integralCALC, how is -2 not in the domain? There is a left-hand portion of this function, and -2 is the max on the interval (infinity, 0). P.S. I love your explanations, they are concise and easy to follow. Keep up the good work.

[@jdcis2smart]

Nathan Tonning I think she made a mistake. The domain for the original function is all real numbers except 0. You may plug in any number into x^1/3 and yield a real number while x^-2/3 turns into 1/(x^2/3) where the only value that makes this part of the equation undefined is 0.

[@nathantonning]

jdcis2smart She probably meant the function has no absolute critical numbers. I thought of this after watching her video on identifying the extrema of a function. Thanks for the reply.

[@shaojunjia6654]

Nathan Tonning, I agree with you. I also have the same doubt.

[@user-el6og2tc2f]

i got it now after some processing you have not not mentioned it any way thank you so much for explaining

[@yalchin007]

This function behaves as mad near a zero point, for example if x = -0.00000000000000000000001, it flies to - cosmos ..))

[@subaccount7212]

how about the equation y=x^4+x^3+3x^2-1 what is the critical points here. I am having a hard time solving for this problem and I don't know how to even get it

[@ShyllaDevera]

still needed?

[@mubashirfaroqi]

I have a question regarding 3 or 4 critical points how can there be 3 or 4 or 5 critical points . Please answer me . That will be your kindness Thankyou

[@kristakingmath]

There can be an infinite number of critical points. A critical point occurs every time the function changes direction from increasing to decreasing, or vice versa. Think about (and graph) the sine function sin(x). That function extends infinitely in both directions, and changes direction an infinite number of times, and each of those changes is a critical point.

[@david-yt4oo]

why is the graph "only defined for positive x values"?, wouldn't this be different since it's a cubed root?

[@awesomewinter3103]

the graph in the video doesn't represent the function.

[@atilla718]

I hate math so so so so so so so so so so much I couldn't even put it in words

[@williamchen9496]

I dont get it. the number droping from nowhere

[@mdatik10]

What is definition of the Critical point??

[@chandrikashrestha]

An interior point of the domain of a function f where f' is zero or undefined is called a critical point of f.

[@mmooooorr]

cubicroot(x-7) find inflection point

[@kristakingmath]

Start by treating it as (x-7)^(1/3), and then finding the second derivative. :)

[@regaltyrones5676]

woooow thank y very moch

[@Guessnought]

still confusing as balls. that being said, this kind of problem is good for a notecard as it incroparates multiple lessons into one. and at least it tests me on what i already know while helping me learn something new. other examples given by other tutors are too basic and dont really prepare me for the hellscape that is college calculus.

[@carterboelke6201]

Great video, but she never actually found the critical points of the function. Yes, there is no maximum but there is a minimum and she never solved for the point.

[@shubhamkashyap9279]

If function is not DIFFIRENCIALBLE then how you gonna find extremums! I hate to write maths in English

[@shubhamkashyap9279]

Ok

[@muhammadabsar462]

I love you. You are so nice>!!!!

[@surajtiwari2614]

Voice is low, it needs calm environment or phone with good speaker to be able to hear it.

[@jefreyquiroz2781]

Then don't watch the video, she actually did a really good job at teaching.

[@user-el6og2tc2f]

i do not understand you please explain slowly with writing details

[@user-el6og2tc2f]

it was a nice example but how did you do ) 1+2x^-1

[@jeannethebeautiful]

-1 exponent can also be rewritten as (-3/3). When you distribute the entire piece that is in the front, it will revert back to (2/3)x^-(5/3)

[@thetablaman24]

Thodi dhire English bolo kuch samaj ni aa ra

[@chandrikashrestha]

Usko bhi hindi samajh nhi aara 😂

[@2012javad]

lol, how did you factor again? just Stop, this is what i hate on college profs and some youtubers on this because they assume I should know already, HEY if I know I wouold not be here. TRUST ME

[@wengeance8962]

Yes, you should be assumed to know how to factor before learning calculus

[@kylenason]

If you don't know how to factor then look up some videos on factoring and maybe look at some different methods on how to go about factoring.

[@2012javad]

@@wengeance8962 thank god you do!