Question

If $f(x)=|x{|}^3,$ then $f^{\prime }(0)$ is equal to

• A. 0
• B. 1
• C. $f^{\prime }(1)$
• D. $f^{\prime }{}^{\prime }(1)$

Answer 1

Answer: (A)

$f(x)=|x{|}^3$
$f(x)=\{\begin{array}{cc}{x}^3,& x>0\\ 0,& x=0\\ -x^3,& x<0\end{array}$
$\Rightarrow$ $f^{\prime }(x)=\{\begin{array}{cc}3x^3,& x>0\\ 0,& x=0\\ -3x^2,& x<0\end{array}$