Math Problem Solver

Let f : [a, b] → R be bounded on [a, b], c ∈ (a, b), n ∈ N,

n ≥ 2, and

g(x) := (x − c)

n

f(x).

a. Show that g(x) is differentiable at x = c.

b. Give an example of a bounded function f such that g

′

(x)

is not continuous at x = c.