Exam 3 - Calculus - 9 Questions | MATH 1120, Exams of Calculus

Download Exam 3 - Calculus - 9 Questions | MATH 1120 and more Exams Calculus in PDF only on Docsity! Math 1120, Section 4 Calculus Test 3 November 24, 2008 Name The total number of points available is 137. Throughout this test, show your work. 1. (15 points) Consider the function f(x) = (x2 − 4x + 4)e2x. (a) Use the product rule to find f ′(x). (b) List the critical points of f . (c) Construct the sign chart for f ′(x). (d) Write in interval notation the interval(s) over which f is increasing. 2. (15 points) Consider the function f(x) = ln[(2x2 + 3)(7x− 2)(x2 − 4)]. (a) Recalling that ln(x) is defined precisely when x > 0, find the domain of f . (b) Let g(x) = (2x2 +3)(7x− 2)2(x2− 4)3. Use logarithmic differentiation to find g′. You need not simplify your answer. 1 Math 1120, Section 4 Calculus Test 3 3. (15 points) Consider the function f(x) = ln(x2 + 4). (a) Find the domain of f . (b) Find both f ′(x) and f ′′(x). (c) Build the sign chart for f ′′(x). (d) Does f have an absolute maximum or and absolute minimum? Is so, which? ... and where? (e) Find an interval over which f is increasing. As usual, to get credit for this, you must show your work. (f) Does f have any inflection points? (g) Use the information from part b. to find the intervals where f is concave upwards. (h) Sketch the graph of f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... ...... 2