Use the given graph of f to find a number ♂ such that if |x − 1] < ♂ then |f(x) − 1] < 0.2. - δ = 1.2 1 0.8 f 0.7 x 1 1.1

Consider the function f which is given on its domain (0, 0) by f(x) = 18x2 – (36x + 9) In(x) . | • Find the number c in the domain of f at which f" is zero or undefined and give its exact value in the first column of the table below. The second column consists of several drop-down menus. Do the following: for each of the given intervals, state if the graph of f is concave up or concave down on that interval; state whether or not c is an inflection point of the graph of f. behavior 0 c concave upward

Consider the function. f(x) = ¹ + 10 Determine the intervals on which f is increasing, decreasing, concave up, and concave down. (Give your answer as an interval in the form (, ). Use the symbol oo for infinity, U for combining intervals, and an appropriate type of parenthesis "(".")", "[","]" depending whether the interval is open or closed. Enter if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if no such intervals exists.) f is increasing on: f is decreasing on: f is concave up on: fis concave down on: Identify the asymptotes of f. (Give your answer as a comma-separated list of equations. Express numbers in exact form. Use symbolic notation and fractions where needed. Let y = f(x) and give any asymptotes in the form of an equation in terms of x and y. Enter DNE if no such asymptote exists.) vertical asymptote(s): horizontal asymptote(s): Use the graphing utility to graph f. f(x) = X desmos

Graph the following function. Determine the interval(s) for 2 which f(x) > 0: f(x) = X 4x