Calculus 1: Graphing and 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 the critical points of the following function

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

Use the 2nd Derivative Test to find the inflection points and intervals of concavity for the following function

$f(x) = x^{3}(x - 4)$

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 all relative maximum and minimum values for the following function

$f(x) = x^4 - 32x^2 + 256$