4, A function f: R2 R has all second order partial derivatives continuous. At th

Question

4, A function f: R2 R has all second order partial derivatives continuous. At the points (1,1), ,1), (1) and (-1,-1), one knows the following values of f and its derivatives: 1,1-20 022 0 0 03-4 (-1,1)0 0 003-1 (-1,-1)-20 0 04-3 4 (a) How many of these points are critical points of f(x, y)? (circle one): (A) 1; (B) 2; (C) 3 (D) 4; (b) At how many of these critical points does f(x, y) have a local minimum? (circle one): (A) 0; (C) 2; (D) 3; (c) At how many of these critical points does f(x, y) have a local maximum? (circle one): (A) 0; ( (C) 2; (D) 3; (d) At how many of these critical points does f(x, y) have a saddle point? (circle one): (A) 0; (B) (C) 2; (D) 3;

Explanation / Answer

The points at which the first derivative is zero or does not exist is called stationary point. for the given function we have three critical points

a) option C - 3

b)option B -1

c)option C-2

d)option A-0

saddle point is a point at which no extrema occurs

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