2nd Derivative Test

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

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

Find all points of inflection and discuss the concavity over different intervals for the following function

$f(x) = x^3 - 6x^2 + 12x$

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

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