Given the function:
[tex]g(x)=|x+5|-|x-9|[/tex]
Using the absolute value rules
So, the function will be written as follows:
[tex]f(x)=\begin{cases}-14;x\le-5 \\ 2x-4;-5So, we will check the points x = -5, x = 9
Because the function has corners at these points
So, f'(x) will be:
[tex]f^{\prime}(x)=\begin{cases}0;x\le-5 \\ 2;59\end{cases}[/tex]
As shown, the middle function is not equal to the function on the sides
So, the answer will be:
g(x) is not differentiable at x = -5, 9
