Basic Analysis I — Real Analysis · Problem 4.3.3

The Derivative — Jiri Lebl

Mathematics — Real Analysis · higher-derivatives-absolute-value-cubed

Problem

Let

f(x) \mathrel{\mathop:}= |x|^3

. Compute

f'(x)

and

f''(x)

for all

x

, but show that

f^{(3)}(0)

does not exist.