How to Find Critical Numbers

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

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

Draw a rough graph of the following function using the critical numbers

$f(x) = \frac{2}{3}x^3 + \frac{9}{2}x^2 - 5x - 17$

Find the inflection points for the following function and determine intervals of concave up and concave down on the graph

$f(x) = \ln{(1 - \ln{(x)})}$