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### Assignment 10

Find the extreme of the function:

without using the sign of the first derivative or the second derivative.

### Solution

In order to find candidates for extremes we have to differentiate the function and make it equal to :

thus:

This equation has the solutions:

or

A closer look at the cubic equation shows that its graph goes from left under to upper right.

For this reason the graph will have a minimum for and a maximum for , see the figure.

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