How to tell if a function is differentiable on an interval?

To see this, consider the everywhere differentiableand everywhere continuous function g(x) = (x-3)*(x+2)*(x^2+4). To prove that g' has at least one zero for x in (-∞, ∞), notice that g(3) = g(-2) = 0. By Rolle's Theorem, there must be at least one c in (-2, 3) such that g'(c) = 0. as example 

The answer would he -4,-2 because the points are just on the opposite side. since the x axis is +4 it's going to he -4 and since the y axis is -2 it stays there because whaen rotated it stays in the third quadrant

Is it multiple choice