Chapter 4, Problem 28RE

In each part, find all critical points, and use the second derivative test (where possible) to classify them as relative maxima, relative minima, or neither.

(a) $f\left(x\right)=x^{-1/2}+\frac{1}{9}{x}^{1/2}$

(b) $f\left(x\right)=x^2+8/x$

(c) $f\left(x\right)={\sin }^{2}x-\cos x,0\le x\le 2\pi$