Question

Need help with this conceptual cal 3 question: Determine whether the following statement is true and give an explanation or counterexample. Assume that f is differentiable at the points in the question.

a) The fact that f_x(2,2) = f_y(2,2) = 0 implies that f has a local maximum, local minimum, or saddle point at (2,2).

True or false, and why?

My book says it's true but doesn't give an explanation.

Answer 1

@hartnn

Answer 2

Hmmmmmm. Don't know sorry.

Answer 3

@ganeshie8

Answer 4

watch this between `15-25` minutes
http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-9-max-min-and-least-squares/