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Proof of absolute maximum and minimum

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.

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.