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# 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

##### Solution Summary

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

##### Solution Preview

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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