Basic Analysis I — Real Analysis · Problem 4.2.13

The Derivative — Jiri Lebl

Mathematics — Real Analysis · differentiability-endpoint-limit

Problem

a) Prove Proposition 4.2.10. b) Suppose

f : (a,b) \to \mathbb{R}

is continuous, and suppose

f

is differentiable everywhere except at

c \in (a,b)

and

\lim_{x \to c} f'(x) = L

. Prove that

f

is differentiable at

c

and

f'(c) = L