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Unformatted text preview: Create assignment, 57321, Homework 22, Apr 18 at 1:41 pm 1 This printout should have 8 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. CalC4c08c 50:03, calculus3, multiple choice, < 1 min, wordingvariable. 001 The graphs of the derivative of functions f, g and h are shown in 4 f : g : h : Use these graphs to decide which of f, g and h have a local minimum on (0 , 4)? 1. only f and g correct 2. only f 3. only g 4. only h 5. only g and h 6. only f and h 7. f, g, and h Explanation: By the First Derivative test, a differentiable function F will have a (i) a local maximum at x if F ( x ) = 0 and the sign of F ( x ) changes from positive to negative as x passes through x ; (ii) a local minimum at x if F ( x ) = 0 and the sign of F ( x ) changes from negative to positive as x passes through x . When F is given by its graph, therefore, we need to look for the xintercepts of the graph of F and then check if the graph of F is decreasing (for a local maximum) or increas ing (for a local minimum) as the graph passes through an xintercept. Applying these criteria to f, g and h we see that the graphs of all of f , g and h cross the xaxis at least once in (0 , 4), but because of the way these graphs change sign only f and g have a local minimum on (0 , 4). keywords: local maximum, first derivative test, graph, local extrema CalC4c18c 50:03, calculus3, multiple choice, < 1 min, wordingvariable....
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This note was uploaded on 03/20/2008 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas at Austin.
 Spring '06
 McAdam

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