The derivative of `f(x)=3|2+x|` at the point `x_0=-3` is

Options

A. 3
B. `-3`
C. 0
D. does not exist

Answer

B

Explanation

Given , `f(x)=3|2+x|`
`or f(x)={(3(2+x)",",x ge -2),(-3(2+x)",",x le -2):}`
On differentiating,
`f'(x)={(3",",x ge-2),(-3",",x le-2):}`
At `x=-3, f'(-3)= -3`