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### Assignment 4

Determine the extreme of the function:

and verify whether it is a maximum or a minimum by using the second derivative.

### Solution

In order to find the candidates of extremes we have to calculate the derivative of the function and solve the following equation:

thus:

and this equation has the solution:

or

The second derivative is:

For the second derivative is negative and thus there is a maximum for .

For the second derivative is positive and thus there is a minimum for .

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