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!
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