The derivative of (f(x) = |x|^{3}) at (x = 0) is | MATH - DERIVATIVE AT A POINT, STANDARD DIFFERENTIATION | SolveeIt | Solveeit

Today, August 18

Question

The derivative of $f(x) = |x|^{3}$ at $x = 0$ is

A

0

B

1

C

–1

D

Not defined

Answer

0

Explanation

Solution

$f(x) = \left{ \begin{matrix} x^{3} & , & x \geq 0 \

x^{3} & , & x < 0 \end{matrix} \right.\ $and$ f^{'}(x) = \left{ \begin{matrix} 3x^{2} & , & x \geq 0 \
3x^{2} & , & x < 0 \end{matrix} \right.\ $

$f^{'}(0^{+}) = f^{'}(0^{-}) = 0$