Finding Critical Points

For the following function draw a rough sketch of the graph for the 3 cases

$f(x) = \frac{(x - a)}{(x - b)(x - c)}$

Case 1: a < b, c

Case 2: b < a < c

Case 3: b, c < a

Find and classify the critical points of the following function

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

Find the critical numbers for the following function

$f(x) = \ln{(x^{2})} + 1.5x$

Find the critical numbers of the function

$f(x) = x^2 - 4x$