Question

The derivative of $f\left(x\right)=3|2+x|$ at $x=-3$ is

• A. $3$
• B. $-3$
• C. $0$
• D. does not exist

Answer 1

The correct option is B $-3$

$f\left(x\right)=3|2+x|$

$\because |2+x|=\{\begin{array}{c}-(2+x),x<-2\\ 2+x,x\ge -2\end{array}$
For $x=-3$
$f\left(x\right)=-3(2+x)$
$\therefore f^{\prime }\left(x\right){|}_{x=-3}=-3$