Posted by Ky on Sunday, March 6, 2011 at 7:56pm.
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.

Calculus  drwls, Sunday, March 6, 2011 at 10:20pm
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.