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2.9 Section http://www.webassign.net/v4cgijrmace2@ncsu/student.pl?n=200811... WebAssign Section 2.9 (Homework) MACE JOHN RANDALL MA 141, section 007, Fall 2008 Instructor: Kyle Thompson Current Score: 13.5 out of 13.5 Due: Saturday, October 4, 2008 10:03 PM EDT Description What Does f ' Say about f ? The due date for this assignment is past. Your work can be viewed below, but no changes can be made. 1. [SCalcCC2 2.10.02.] 2/2 points The graph of the derivative f ' of a function f is shown. (a) On what interval(s) is f increasing? (Select all that apply.) (5,6) (2,4) (0,1) (4,6) (0,2) (3,5) (1,3) On what interval(s) is f decreasing? (Select all that apply.) (4,6) (1,3) (0,2) (0,1) (5,6) (3,5) 1 of 7 PDF created with pdfFactory Pro trial version www.pdffactory.com 11/20/2008 10:15 PM Section 2.9 http://www.webassign.net/v4cgijrmace2@ncsu/student.pl?n=200811... (2,4) (b) At what value(s) of x does f have a local maximum? (Select all that apply.) 2 5 4 3 1 6 0 At what value(s) of x does f have a local minimum? (Select all that apply.) 1 2 5 0 4 6 3 (c) If it is known that f(0) = 0, sketch a possible graph of f. (Do this on paper. Your teacher may ask you to turn in this work.) 2. [SCalcCC2 2.10.08.] 2/2 points A particle is moving along a horizontal straight line. The graph of its position function (the distance to the right of a fixed point as a function of time) is shown. 2 of 7 PDF created with pdfFactory Pro trial version www.pdffactory.com 11/20/2008 10:15 PM Section 2.9 http://www.webassign.net/v4cgijrmace2@ncsu/student.pl?n=200811... (a) When is the particle moving toward the right? (Select all that apply.) (4,6) (3,6) (0,3) (2,4) (0,2) When is the particle moving toward the left? (Select all that apply.) (0,3) (4,6) (3,6) (2,4) (0,2) (b) When does the particle have positive acceleration? (Select all that apply.) (0,4) (3,6) (0,3) (2,6) When does the particle have negative acceleration? (Select all that apply.) (0,3) (0,4) (2,6) (3,6) 3 of 7 PDF created with pdfFactory Pro trial version www.pdffactory.com 11/20/2008 10:15 PM Section 2.9 http://www.webassign.net/v4cgijrmace2@ncsu/student.pl?n=200811... 3. [SCalcCC2 2.10.12.] 3.5/3.5 points The graph of the derivative f ' of a continuous function f shown. is (a) On what interval(s) is f increasing? (Select all that apply.) (6,8) (8, ) (3,5) (1,6) (5,7) (0,2) (0,1) (7, ) (2,3) On what interval(s) if f decreasing? (Select all that apply.) (6,8) (0,1) (2,3) (3,5) (1,6) (0,2) (7, ) (5,7) (8, ) (b) At what value(s) of x does f have a local maximum? (Select all that apply.) 6 7 8 4 of 7 PDF created with pdfFactory Pro trial version www.pdffactory.com 11/20/2008 10:15 PM Section 2.9 http://www.webassign.net/v4cgijrmace2@ncsu/student.pl?n=200811... 0 3 1 At what value(s) of x does f have a local minimum? (Select all that apply.) 1 7 6 8 0 3 (c) On what interval(s) is f concave upward? (Select all that apply.) (0,2) (3,5) (5,7) (2,3) (7, ) On what interval(s) is f concave downward? (Select all that apply.) (0,2) (5,7) (7, ) (2,3) (3,5) (d) Determine the x-coordinate(s) of the point(s) of inflection. (Select all that apply.) 1 8 7 2 5 3 5 of 7 PDF created with pdfFactory Pro trial version www.pdffactory.com 11/20/2008 10:15 PM Section 2.9 http://www.webassign.net/v4cgijrmace2@ncsu/student.pl?n=200811... (e) Assuming that f(0) = 0, sketch a graph of f. (Do this on paper. Your teacher may ask you to turn in this work.) 4. [SCalcCC2 2.10.22.] 1/1 points If f '(x) = e-x , what can you say about f? f is decreasing on f is increasing on f does not exist 2 5. [SCalcCC2 2.10.24.] 4/4 points Let f(x) = x4 - 2x2. (a) Use the definition of a derivative to find f '(x) and f ''(x). f '(x) = 4x^3 - 4x f ''(x) = 12x^2 -4 4x^3 - 4x 12x^2 - 4 (b) On what interval(s) is f increasing? (Select all that apply.) (1, ) (- ,-1) (0,1) (-1,0) On what interval(s) is f decreasing? (Select all that apply.) (- ,-1) (1, ) (-1,0) (0,1) 6 of 7 PDF created with pdfFactory Pro trial version www.pdffactory.com 11/20/2008 10:15 PM Section 2.9 http://www.webassign.net/v4cgijrmace2@ncsu/student.pl?n=200811... (c) On what interval(s) is f concave upward? (Select all that apply.) On what interval(s) is f concave downward? (Select all that apply.) 6. [SCalcCC2 2.10.26.] 1/1 points The graph of a function f is shown in red. Which graph is an antiderivative of f? a (in black) b (in blue) c (in yellow) 7 of 7 PDF created with pdfFactory Pro trial version www.pdffactory.com 11/20/2008 10:15 PM

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