Question

Write the derivative of f (x) = 3 |2 + x| at x = −3.

Answer 1

$$\begin{gathered} \text{Let x = -3} \\ \text{We know:} \\ \text{-3<-2} \\ \text{Thus, we have:} \\ \text{x<-2} \\ \text{It gives x+2<0.} \\ \therefore \left|2+x\right|=\left|x+2\right|=-\left(x+2\right)=-x-2 \\ f\left(x\right)=3\left|2+x\right|=3\left(-x-2\right)=-3x-6 \\ f\text{'}\left(x\right)=-3\frac{d}{dx}\left(x\right)-\frac{d}{dx}\left(6\right)=-3 \end{gathered}$$