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## Homework Statement

Using the derivative f'(x) = (x-1)[tex]^{2}[/tex](x+2)[tex]^{2}[/tex] answer the following:

a) What are the critical points of f?

b) On what intervals is f increasing or decreasing?

c) At what points, if any, does f assume local maximum and minimum values?

## Homework Equations

n/a

## The Attempt at a Solution

From strictly observing the derivative and using the quadratic equation to check, the critical points are x=1 and x=(-2). Once I pick a number within each of the intervals (-inf, -2), (-2, 1), and (1, inf) and implement it into the equation, I consistently get positives. By definition of Corollary 3: First Derivative Test for Monotonic Functions, the equation would be increasing on every interval; therefore, making a line. The problem is, when I graph the answer to check my solution, I notice a critical point at x=(-.05). Where did this CP come from and how do I figure it out algebraically?

Any guidance would be greatly appreciated.