# How do you find the critical numbers of 1/(t^2+3)?

May 26, 2017

A critical number for $f \left(t\right)$ is a solution of the equation:

$f ' \left(t\right) = 0$

In our case:

$f ' \left(t\right) = - \frac{2 t}{{t}^{2} + 3} ^ 2$

So the only critical point of the function is for $t = 0$

Since $f ' \left(t\right) > 0$ for $t < 0$ and $f ' \left(t\right) < 0$ for $t > 0$ such point is a local maximum.

graph{1/(x^2+3) [-2.5, 2.5, -1.25, 1.25]}