Calculus 1 Question Derivatives

Question

Explain why the following functions do not have derivatives at the designated points.

a) f(x) = |x−1|, x = 1

Answer 1

the derivative is the slope of the function

f(x) = the absolute value of (x-1) has slope -1 for x<1 and slope = +1 for x>1. But at x=1 there is no tangent line to the function. It's undefined. It could be anywhere between -1 to +1.