Question

If ​f(x) = 3$\left|x+2\right|$, then f '(-3) = ___________________.

Answer 1

We know

$\left|x+2\right|=\left\{\begin{array}{ll}x+2,& x\ge -2\\ -\left(x+2\right),& x<-2\end{array}\right.$

$\therefore f\left(x\right)=3\left|x+2\right|=\left\{\begin{array}{ll}3\left(x+2\right),& x\ge -2\\ -3\left(x+2\right),& x<-2\end{array}\right.$

$\Rightarrow f\text{'}\left(x\right)=\left\{\begin{array}{ll}3,& x\ge -2\\ -3,& x<-2\end{array}\right.$

For x < −2, $f\text{'}\left(x\right)=-3$

$\therefore f\text{'}\left(-3\right)=-3$



If ​f(x) = 3$\left|x+2\right|$, then f '(−3) = ____−3____.