Consider the polynomial function f(x) = x^3 − 2x^2 + x − 2

Question

By hand, using calculus skills, find all critical points of f(x). Find the absolute extrema of f(x) on the interval [0, 1], label them appropriately.

Answer 1

The derivative of the function is f'(x)=3x^{2}-4x+1 which has zeroes at the points x=1/3 and x=1. Using the criterion of the first derivative and by checking the endpoints of the interval [0,1] you can identify the extrema that you are looking for.