What are critical points?

Critical points are one of the best things we can do with derivatives, because critical points are the foundation of the optimization process. Optimization is all about finding the maxima and minima of a function, which are the points where the function reaches its largest and smallest values. And if we know which values maximize function and which ones minimize it, that has all kinds of real-world applications.

In order to find critical points, which are the points where the function might have extrema, we just take the derivative of the original function, set that derivative equal to 0, and then solve that equation for x. That gives us the critical points of the function. Then, we can test those critical points to determine whether they represent maxima, minima, or neither.

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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?!”

[ryanboguslavsky]

Extremely understandable. I wish this was recommended instead of Kan Academy.

[JamesJon]

That feeling when you've finally found how to handle your neighbor's request to relate their dog's food quantity to the moon's current distance. #tearsofrelief #toorelatable

[EliteRowmaster]

That example was brilliant comic relief. Such a great explanation keep it going!!

[animeleepocket]

Incredible series of videos. I think this should be in the repertoire of all struggling students.

[isaacnunezfielsted]

Absolutely outstanding pedagogical classes, it's one of my favorite virtual math online

[JuanyJuanes]

i literally looked at the topic for my online math class tonight, logged into the web conference, and muted it to watch your video.

[DeepakGupta-cmbx]

I just can't resist saying it one more time, Krista, U simply are the best Math teacher Expressing a concept with simplicity is an art - And it come naturally to U !:) Deepak

[rafaelgpontes]

Love your videos. They remind me of when I studied calculus. Keep up the great work! Cheers from Brazil! o/

[timothy]

This channel has way better script, structure, presentation, and production quality than that overrated Khan Academy.

[bunny-bunny-bunny]

this is really good stuff, the script is well organized and visuals complement it well! super helpful to go over the lecture again. thanks & keep it up <3

[vdwest]

@Krista King Keep making videos. I believe you have found your calling!

[shrimaydutta]

Helped me clearing my
Love from India.

[vijaykaran]

I want to just say that it is really awesome

[ZahirKhan-]

Loved the way you explained!! Subscribed

[DittyDafku]

Not gonna lie, this was an impressive video. Very very easy to follow through. I will not shit on Khan however because it is thanks to them that I am passing.

[esamh]

Very Good Krista. can you help me in PDE specifically in Heat and Wave equations ?? Thank you.

[mellow]

Thanks for making Bus Calc less of a headache for me!

[azizghalib]

How could the minimum distance from the moon ever be -3/4?
Shouldn't there be a restricted domain?

[nicholascosta]

Hey, was was right, thanks again for getting me to RIT!

[masha]

what indicates that x=-3/4 is the minimum amount of food for the dog ?