36. A number a is called a fixed point of a function f if f(a) = a. Prove that if f'(x) # 1 for all real numbers x, then f has at most one fixed point.17-18 Show that the equation has exactly one real root. 17. 2x + cos x = 0 18. x' + ex = 0 19. Show that the equation x3 - 15x + c = 0 has at most one root in the interval [-2, 2]. 20. Show that the equation x4 + 4x + c = 0 has at most two real roots. 21. (a) Show that a polynomial of degree 3 has at most three real roots. (b) Show that a polynomial of degree n has at most n real roots. 22. (a) Suppose that f is differentiable on R and has two roots. Show that f' has at least one root