Locate and classify all critical points for the given function.
-$f(x, y)=1-\left(x^{2}-y^{2}\right)$
A) Minimum of 1 at $(0,0)$
B) Saddle point at $(0,0)$
C) Maximum of 1 at $(0,0)$
D) None of the above is correct.

Question

Quizplus · Accepted Answer

The critical point is found by setting the gradient to zero, which gives $(0,0)$. The second derivative test shows that the Hessian determinant is negative, indicating a saddle point.

Locate and Classify All Critical Points for the Given Function f(x,y)=1−(x2−y2)f(x, y)=1-\left(x^{2}-y^{2}\right)f(x,y)=1−(x2−y2)

Locate and Classify All Critical Points for the Given Function $f(x, y)=1-\left(x^{2}-y^{2}\right)$