# Find the extreme values of the function f(x)=(x^2-1)/(x^2+1) on the interval [-5,5].

Find the extreme values of the function
$f\left(x\right)=\frac{{x}^{2}-1}{{x}^{2}+1}$
on the interval [-5,5].
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Abigayle Lynn
$f\left(x\right)=\frac{{x}^{2}-1}{{x}^{2}+1};\left[5,-5\right]$
Find critical point
${f}^{\prime }\left(x\right)=\frac{{f}^{\prime }g-{g}^{\prime }f}{{g}^{2}}=0\phantom{\rule{0ex}{0ex}}=\frac{2x\left({x}^{2}+1\right)-2x\left({x}^{2}-1\right)}{\left({x}^{2}+1{\right)}^{2}}=0\phantom{\rule{0ex}{0ex}}=\frac{4x}{\left({x}^{2}+1{\right)}^{2}}=0\phantom{\rule{0ex}{0ex}}f\left(-5\right)=\frac{\left(-5{\right)}^{2}-1}{\left(5{\right)}^{2}+1}=\frac{25-1}{25+1}=\frac{24}{26}$