The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval (0,1) where f'(c)=0.

Question

f(x) = x3 - 2x2 + x, [0, 1]

Round your answer to two decimal places.

Answer 1

First, be sure that f(0)=f(1). It does

since f'(x) = 3x^2-4x+1 = (3x-1)(x-1)

just find a value in the interval [0,1] where f'(x) = 0. Now it's just algebra. The calculus is done.