Chapter 4.2, Problem 4ES

(a) Use both the first and second derivative tests to show that $f\left(x\right)={\sin }^{2}x$ has a relative minimum at $x=0$ .

(b) Use both the first and second derivative tests to show that $g\left(x\right)={\tan }^{2}x$ has a relative minimum at $x=0$ .

(c) Give an informal verbal argument to explain without calculus why the functions in parts (a) and (b) have relative minima at $x=0$ .