#8-9 Name: Summer 2017 MTH 145 Due Date: Tuesday, July 11, 2017 This assignment is for Section 4.3 4.5. Please put your answers on the lines provided. Your understanding should be communicated using correct steps in your solution. Show work below to earn credit. 1. Given the graph of f , find the following. (a) abs max(s) on [3, 1] abs min(s) on [3, 1] (b) inc interval(s) dec interval(s) (c) critical numbers (x-vals) (d) local max(s) local min(s) (e) concave up concave down (f) inflection point(s) 2. Sketch the graph of a function f that satisfies the following conditions. Assume the curve is continuous everywhere except at vertical asymptotes. (1) f (1) = 2 (2) f 0 (x) > 0, if x < 3 and 1 < x < 1 (3) f 0 (x) < 0, if 3 < x < 1 and x > 1 (4) f 00 (x) > 0, if x < 3 and x > 3 (5) f 00 (x) < 0, if 3 < x < 1 and 1 < x < 3 (6) lim f (x) = x1 (7) lim f (x) = 0 x (8) lim f (x) = 2 x x , find the critical numbers by hand without the calculator. Use x2 + 17 the First Derivative Test to find the intervals on which f is increasing or decreasing and the local maximum and minimum values. Fill in the number line with test results. Give exact answers, not decimal approximations. Show work to earn credit. 3. Given the function f (x) = CN x= number line <-> decreasing interval(s) increasing interval(s) local max(s) local min(s) (list x and y-vals) 4. Given the function f (x) = 6x4/3 35 x5/3 , find the potential inflection points by hand without the calculator. Use the Second Derivative Test to find the intervals on which f is concave up or down and the inflection points. Fill in the number line with test results. Show work to earn credit. PIP x= number line <-> concave up interval(s) inflection point(s) concave down interval(s) (list x and y-values)