Use the Intermediate Value Theorem and Rolle's Theorem to prove that the equation has exactly one real solution. x + x' + x+2 =0 f ---Select--- v differentiable for all x. Because f(-1) ? v 0 and f(0) ? |0, the Intermediate Value Theorem implies that f has at least one value cin [-1, 0] such that f(c) = If fhad 2 zeros, f(c,) = f(c, ) = 0, then Rolle's Theorem would guarantee the existence of a number a such that f'(a) = f(c2) - f(c,) = But, f'(x) = and f'(x) ? |0 for all x. So, f(x) = 0 has exactly one real solution