Calculus 1: Graphing and Critical Points

Find the critical points of the function

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

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

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

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 all points of inflection and discuss the concavity over different intervals for the following function

$f(x) = x^3 - 6x^2 + 12x$

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

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