# Proof of absolute maximum and minimum

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I would like help with the following problem:

Find with proof the absolute maximum and minimum values of

f(x) = x^4 + 2x^2 - 4 on the interval [0,3].

There's a hint saying that you can prove this using the mean value theorem.

Thanks for all of your help.

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:46 pm ad1c9bdddfhttps://brainmass.com/math/complex-analysis/proof-absolute-maximum-minimum-60954

#### Solution Preview

Hi, here is the solution

To find the absolute maxima and minima of the function

f(x) = x^4 + 2x^2 - 4 on the interval [0,3].

We first take the derivative

f'(x) = 4x^3+4x

and find the roots of the derivative which are

4x(x^2+1) =0

x=0 and x^2 =-1

x=0 , x= +/- i

These are the only critical points of f. We consider the following table of the endpoints and the ...

#### Solution Summary

This shows how to find and prove absolute maximum and minimum values.

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