Question

let f(x)=|x-5|. the derivative of f evaluated at x=5 is

Answer 1

0?

Answer 2

https://www.desmos.com/calculator/8wnzwghydv

Look at the graph above.
On the left side of x=5 you'll see that it's a straight line at a 45 degree angle downward.
It has a slope of -1.

On the right side of x=5 it has a slope of 1.

AT x=5 there is a discontinuity - a sharp corner.
Therefore the derivative does not exist at x=5 for this function.