Locate and classify all critical points for the given function.
-$f(x, y)=5-\left(x^{2}+y^{2}\right)$
A) Maximum of 5 at $(0,0)$
B) Maximum of $\frac{5}{2}$ at $(5,5)$
C) Minimum of 5 at $(0,0)$
D) None of the above is correct.

Question

Quizplus · Accepted Answer

The function $f(x, y)=5-(x^2+y^2)$ is a downward-opening paraboloid. The critical point is at $(0,0)$, where the function achieves its maximum value of 5.

Locate and Classify All Critical Points for the Given Function f(x,y)=5−(x2+y2)f(x, y)=5-\left(x^{2}+y^{2}\right)f(x,y)=5−(x2+y2)

Locate and Classify All Critical Points for the Given Function $f(x, y)=5-\left(x^{2}+y^{2}\right)$