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# t2125su - Create assignment 57321 Homework 22 Apr 18 at...

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Create assignment, 57321, Homework 22, Apr 18 at 1:41 pm 1 This print-out should have 8 questions. Multiple-choice 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, wording-variable. 001 The graphs of the derivative of functions f, g and h are shown in 4 f 0 : g 0 : h 0 : 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 0 if F 0 ( x 0 ) = 0 and the sign of F 0 ( x ) changes from positive to negative as x passes through x 0 ; (ii) a local minimum at x 0 if F 0 ( x 0 ) = 0 and the sign of F 0 ( x ) changes from negative to positive as x passes through x 0 . When F 0 is given by its graph, therefore, we need to look for the x -intercepts of the graph of F 0 and then check if the graph of F 0 is decreasing (for a local maximum) or increas- ing (for a local minimum) as the graph passes through an x -intercept. Applying these criteria to f, g and h we see that the graphs of all of f 0 , g 0 and h 0 cross the x -axis 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, wording-variable.

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t2125su - Create assignment 57321 Homework 22 Apr 18 at...

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