Show that Rolle's Theorem applies to the given function for the given values of x: x=-1 and x=4 for f(x)=3x-x^2+2.
f(-1) = -2
f(4) = -2
f(x) is differentiable in the interval, so the conditions are met, and the theorem applies.
Extra credit:
We want to show that for c somewhere in [-1,4] f'(c) = 0.
f'(x) = 3-2x
f'(x) = 0 when x = 3/2
3/2 is within the interval [-1,4], so the theorem does indeed work.