Suppose f is differentiable at a and f(a) # 0. (a) Prove |f| is differentiable at a by using that |f| = Vf2. What are the possible values of |fl'(a)? (b) Give a counterexample that shows the...

Extracted text: Suppose f is differentiable at a and f(a) # 0. (a) Prove |f| is differentiable at a by using that |f| = Vf2. What are the possible values of |fl'(a)? (b) Give a counterexample that shows the conclusion need not hold if f(a) = 0. Identify where your calculations for (a) fail in this case.