Answer:
There are 2 points where f'(x) = 0
At x = 0, and at x = 5/π
Step-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) = 0
Evaluate 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)/2
f(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 = 0
5x = π, so x = 5/π
