Calculus 1: Graphing and Critical Points

Find the critical points of the function

$f(x) = \frac{5}{{(x^2 - 4x)}^2}$

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 points of the following function

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

Find the critical numbers for the following function

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

Find the critical numbers of the function

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

Find the critical numbers for the following function $f(x) = x^{\frac{2}{3}}$

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

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

Find the inflection points and intervals of concavity for the following function

$y = \frac{x^2 + 1}{x^2}$

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

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

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

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

Find the relative extrema for the following function on the given interval

$f(x) = \frac{2x}{x^2 + 1}$ , $[-2, 2]$

Find the absolute extrema of the following function on the given interval

$h(x) = \frac{x}{x - 2}$ , $[3, 5]$

Find all relative maximum and minimum values for the following function

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