(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the absolute max/min of the function on it's interval.

[tex]f(x)=\frac{x^2-4}{x^2+4}[/tex]

Interval: [-4,4]

2. Relevant equations

3. The attempt at a solution

[tex]f(x)=\frac{x^2-4}{x^2+4}[/tex]

I basically want to find all the critical points, so I set the denominator to zero and found a critical point to be where x = 2i, and x = -2i.

Then I took the derivative of the function as so:

[tex]f'(x) = \frac{2x(x^2+4)-2x(x^2-4)}{(x^2+4)^2}[/tex]

Setting the numerator to zero should find where the derivative is equal to zero, but that expands out to this:

[tex]2x^3+8x-2x^3+8x[/tex]

Which is basically zero anyway. I was going to try to factor out something from the numerator and denominator (if possible) to cancel it out so I could get something, but I thought I would lose solutions doing that. So here is where I am confused? I tried graphing it, thinking that it would just return the line y=0, but my TI-89 just says "not a function or program, error"?

edit: fixed

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# Maximums and Minimums

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