Locate and classify all critical points for the given function.
-A critical point for $f(x, y)=x y+\left(\frac{2}{x}\right)+\left(\frac{2}{y}\right)$ is $\left(2^{1 / 3}, 2^{1 / 3}\right)$. Is this a maximum or minimum? What is the value?
A) Minimum value of $3\left(2^{1 / 3}\right)$
B) Minimum value of $3\left(2^{2 / 3}\right)$
C) Maximum value of $3\left(2^{2 / 3}\right)$
D) Maximum value of $3\left(2^{1 / 3}\right)$

Question

Quizplus · Accepted Answer

The critical point $(2^{1/3}, 2^{1/3})$ is a minimum, and substituting into the function gives the minimum value $3(2^{2/3})$.

Locate and Classify All Critical Points for the Given Function f(x,y)=xy+(2x)+(2y)f(x, y)=x y+\left(\frac{2}{x}\right)+\left(\frac{2}{y}\right)f(x,y)=xy+(x2​)+(y2​)

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