Please explain #19, 20

17. Let f(x) = (x - 3)-2. Show that there is no value of c in (1, 4) such that f(4) - f(1) = f'(c)(4 - 1). Why does this not contradict the Mean Value Theorem? 18. Let f(x) = 2 - |2x - 1). Show that there is no value of c such that f(3) - f(0) = f'(c)(3 - 0). Why does this not contradict the Mean Value Theorem? 19-20 Show that the equation has exactly one real root. 19. 2x + cos x = 0 20. 2x - 1 - sin x = 0 21. Show that the equation x' - 15x + c = 0 has at most one root in the interval [-2, 2]. 22. Show that the equation x4 + 4x + c = 0 has at most two real roots