Twice Means Thrice?

Calculus Level 1

True or False?

$\quad$ A function that is twice- differentiable must also be thrice-differentiable.

True False

2 solutions

Brian Charlesworth
Jan 25, 2017

Consider the function

$f(x) = \begin{cases} \dfrac{x^{3}}{6}, x \ge 0 \\ -\dfrac{x^{3}}{6}, x \lt 0 \\ \end{cases}$

Then $f''(x) = |x|$ , which is not differentiable at $x = 0$ , since $\displaystyle\lim_{x \to 0^{-}} f'''(x) = -1$ and $\displaystyle\lim_{x \to 0^{+}} f'''(x) = 1$ .

Anindya Mahajan
May 31, 2020

Consider the function which you get after integrating abs(x) twice.

Twice Means Thrice?

2 solutions

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