# Calculus 1 absolute minimum and maximum of a function?

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This is the question: Find the absolute maximum and absolute minimum values of f(x)=(x^2-16)/(x^2+16) on the interval [−5,5].

This is the question: Find the absolute maximum and absolute minimum values of f(x)=(x^2-16)/(x^2+16) on the interval [−5,5].

##### 1 Answer

#### Answer:

Please see the explanation.

#### Explanation:

Here is the graph of the expression:

The graph shows that the maximums for the interval occur at the ends of the interval,

Let's see what The Calculus can tell us about it:

Add 0 to the numerator in the form + 16 - 16:

Separate into two fractions:

The first term becomes 1 and the numerator of the second term becomes -32:

Compute the first derivative:

This can only be 0 at

Perform the second derivative test:

This is a minimum.

The absolute maximum is:

You can find that this is 1 by repeated application of L'Hopital's rule or by doing the quotient - remainder substitution that I did.