Concavity Calculus Practice Problem

Find and classify the critical points of the following function

$f(x) = x^3 - 3x^2 - 9x + 2$

Find the critical points of the following function

$f(x) = 6x^5 + 33x^4 - 30x^3 + 100$

Use the second derivative test to find all relative extrema of the following function

$f(x) = \frac{1}{3}x^3 + 2x^2 + 3x$

Find the relative extrema for the following function on the given interval

$f(x) = \frac{2x}{x^2 + 1}$ , $[-2, 2]$