Chapter 14.7, Problem 26E

To determine

(a) Where the function $f$ takes on its minimum value without using the calculus.

(b) That the set of critical points of $f$ consists of the origin and the unit circle $x^2+y^2=1$

(c) That $f$ takes the maximum value on the unit circle by analyzing the function $g\left(t\right)=t{e}^{-t}\left(t>0\right)$