critical points of multivariable functions (KristaKingMath)

In this video we'll learn how to find the critical points (the points where the function changes direction) of a multivariable function. In order to find critical points, we'll need to take partial derivatives of the function with respect to both variables, and then set each of them equal to 0. We'll use the equations together as a system of linear equations (simultaneous equations) to solve for the unique solution, which will be the critical point.

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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?!”

[johnathanaguirre]

This might be the best video about this.

[scoobynicker]

I don't know why my instructor insists on giving me questions that he doesn't cover and also aren't covered in the text book, but at least I have you to teach me.

[troyjohnson]

YES. THANK YOU. AN ENTIRE SEMESTER OF CALC 2 AND ONLY NOW have i learned how to do this thank you for explaining so clearly and effectively.

saved my final (10 hrs from now) fr

[karenlowe]

I love your videos! I love that you start with a big picture overview of what we're going to do, and then your steps are very clear and well-explained. Also, you have a wonderful, calming voice and I have learned so much from your videos. You are the best!

[samiaakbar]

You don't even know how wonderful art of work you have done for the students even after a decade..❤❤

[victorpaesplinio]

Wow! I think your partial derivatives play list will save me in my calc 2 tests

[dougwise]

i dont know how i would survive calculus 3 without this person

[zodiark]

Hell yeah, no fluff, just explanation.

[dynamisarian]

Hello dear, so easily explained in your video and I freaking loved it😍😍

[ThreeDaysGrace]

your so clutch, thank you so much <3

[Camper]

My only confusion on this topic is when there are multiple critical points for the function in which case, i dont know whether i have all the critical points or not after doing some of these methods

[jerryhernandez]

Thanks!!! You just saved me for a quiz

[juanfernandes]

Really thanks for the amazing class! :D

[leoamm]

Thanks for your wonderful videos, that help a lot, in the way please let me know if there any recommendation for more fast understanding, thanks..

[rasulguidry]

at 3:21 could you have set both functions equal to each other, for example 2x+y=x+2y+1?

[coookei]

THANK YOU SO MUCH YOUVE PREPARED ME FOR MY FINAL EXAM TOMORROW

[austinnewton]

So is the point (1/3, -2/3) a minimum using the second derivative test ?

[deeallo]

I have a question I found the value of x and it was two numbers one negative and the other is positive but the problem is that I can’t plug in the negative number to find the value of y because the y formula has a square root so should I consider it as a critical point or what?🤔

[tangpiseth]

What if trying to find the critical point by letting partial df/dx=0 and you find that partial df/dx=1/y^2=0? is the critical point undefined ?

[behonest]

What is the difference between critical point and stationary point in multivariate function