Q:

Can anyone explain the underlined content in the image?

I understood everything except the thing inside the red bracket which states that "The derivative f'(x) can change its sign only at values of x where f'(x) =0 or f'(x) is undefined or f(x) is discontinuous." How can derivative exist at the point wheref(x) is discontinuous and when and how f'(x) can change its sign, i could not get it. Please help!

A:

It just means that for example the derivative could be positive, then it could be undefined and when it is defined again it is negative

