Question

Verify the hypothesis of Rolle's Theorem for the function, f(x)=cosx , [π/2,3π/2]

Answer 1

Rolle's theorem states that for an interval a to b on f(x), if (a,b) is continuous and differentiable, and If f(a) = f(b), then at some point c between a and b the derivative is zero. Take the derivative of cosx (which is -sinx), find the zeros, and then show that at least one of those zeros is on the interval pi/2 to 3pi/2.

Answer 2

The derivative of cosx is -sinx which has a 0 at x = pi, which is certainly between pi/2 and 3pi/2