Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = cos(5x), [π/20, 7π/20] c =

Answer:There are 2 points where f'(x) = 0At x = 0, and at x = 5/πStep-by-step explanation:Rolle's theorem states that for any differentiable function on the interval {a, b}, if f(a) = f(b), then there is at least one point in the interval where f'(c) = 0Evaluate the end points of the interval to see if we can apply Rolle's Theorem...f(π/20) = cos (5π/20) = cos (π/4) = (√2)/2f(7π/20) = cos [5(7π]/20) = cos (35π/20) = cos (7π/4) = (√2)/2 So by Rolle's Theorem, there will be at least one point where f'(c) = 0, so find f'(x)f'(x) = -5sin(5x)find where this equal zero...0 = -5sin(5x)0 = sin(5x)Sin x = 0 at x = 0, and x = π, so we have..5x = 0,  so x = 05x = π, so x = 5/π