Question

Let f(x) = x 5 5 − x 4 + x 3 + 2x 2 − 4x + 1. 1. Find f 0 (x) and factor it into linear factors. 2. Find the critical numbers of f(x) on the open interval (0, 3). 3. Find the local extrema of f(x) on the open interval (0, 3). 4. Find the absolute maximum and absolute minimum values of f(x) on the closed interval [0, 3].

Answer 1

F(0)=1

critical values are

df(x)/dx=0

5x^4-4x^3+3X^2+4x-4=0

Solve this equation

The critical values are 2.5 and 0.294