# How do you find the local max and min for f(x) = (3x) / (x² - 1)?

Dec 16, 2016

$f \left(x\right) = \frac{3 x}{{x}^{2} - 1}$ has no local extrema

#### Explanation:

Find the critical points by equating the first derivative to zero:

$f ' \left(x\right) = \frac{3 \left({x}^{2} - 1\right) - 6 {x}^{2}}{{\left({x}^{2} - 1\right)}^{2}} = - 3 \frac{{x}^{2} + 1}{{\left({x}^{2} - 1\right)}^{2}}$

As the derivative is negative in all the domain of the function, the function is strictly decreasing and has no local extrema.

graph{3x/(x^2-1) [-10, 10, -5, 5]}