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