Question

Sesssion 9, Solution to the problem.
Why are the inequality signs changed from non-strict (x<=0) to strict (x<0) when we take derivative of f(x)?

Answer 1

For example if we have y = |x| where y = x if >=0 or y = -x if x<0, we have
We have a cusp at x = 0, hence the function is not differentiable at x = 0 (no tangent can be drawn at x = 0). Thus the slope (derivative) is only defined when x>0 or when x<0.

Answer 2

I get it now. Thanks for the answer!