Critical Points Calculus

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

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

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

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

Find the critical points of the following function

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