How do you find the local maximum and minimum values of f(x) = (3x) / (x² - 1) using both the First and Second Derivative Tests?

Feb 3, 2016

This function has no local extreme values.

Explanation:

$f ' \left(x\right) = \frac{\left(3\right) \left({x}^{2} - 1\right) - \left(3 x\right) \left(2 x\right)}{{x}^{2} - 1} ^ 2 = \frac{- 3 \left({x}^{2} + 1\right)}{{x}^{2} - 1} ^ 2$

$f '$ is never $0$ and is defined on the whole domain of $f$.

Therefore, $f$ has no critical numbers, so $f$ has no local extreme values.

Because it has no critical numbers, there is nothing to apply the tests to.