Concavity Calculus Practice Problem

Find and classify the critical points of the following function

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

$y = x^{2/3}(2-x)$

Find: A. The critical values of x? B. The x coordinate of the local maximum

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

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