CMIIh

2020-12-24

Find the critical points of the following functions.Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical points.

$f(x,y)=y{e}^{x}-{e}^{y}$

joshyoung05M

Skilled2020-12-25Added 97 answers

To find the critical point, find

For

Therefore y=0

Set

Substitute

Taking ln on both sides,

Thus (0,0) is the ritical point.

1) If D(a,b)>0 and

2) If D(a,b)>0 and

3) If D(a,b)<0 then f(a,b) is saddle point

4) If D(a,b)=0 then this is incobclusive

Here,

The critical point is(0,0)

Thus D(0,0)=-1<0 then f(0,0) is saddle point,

Therefore -1 is saddle point.

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