# Differentiation, Extrema of a Function

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Please show the how to solve the following. Please offer as much explanation as possible. Thanks.

Graph a function on the interval [-2,5] having the following characteristics:

Critical number at x = 0, but no extrema

Absolute minimum at x = 5

Absolute maximum at x = 2

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##### Solution Summary

Differentiation for extrema of a function are provided. The absolute minimums and maximums are provided.

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I assume you have studied derivatives.

The point to pay attention to is to have a critical point at x=0.

It means f'(0)=f''(0)=0 at this point, but, in the simplest case f'''(0) is not 0.

As to the rest of the conditions - ...

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