Question

Determine if Rolle's Theorem applies to the given function f(x)=2 cos(x) on [0, pi]. If so, find all numbers c on the interval that satisfy the theorem.

Answer 1

Rolle's theorem states that a differentiable function that has equal values at two distinct points must have a point somewhere between them where the first derivative is zero.

Rolle's theorem does not apply to that function in that interval, since f(x) decreases from 1 at x = 0 to -1 at pi. There are no two values of x in the [0, pi] interval where the f(x) values are the same.