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F09Graphsample1ANS

F09Graphsample1ANS - The following is a graph of the first...

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The following is a graph of the first derivative f’(x) of a function y = f(x). You may assume f(x) is defined for all real numbers. y Use this graph of f’(x) to answer the 2 y = f’(x) following questions about the graph of f(x). 1 -7-6-5-4-3 2 - 1 1 2 3 4 5 6 7 8 x -2 a. On what interval(s) is the graph of f(x) concave up? ANSWER : The graph of f(x) is concave up on the intervals in which f’’(x) > 0, ie on the intervals in which f’(x) is increasing, that is ( - , -1) and (4,+ ). b. On what interval(s) is the graph of f(x) concave down? ANSWER: The graph of f(x) is concave down on the intervals in which f’’(x) < 0, ie on the intervals in which f’(x) is decreasing, that is ( -1,4). c. Give the x coordinate of the point(s) of inflection. ANSWER: The points of inflection are the points about which the graph changes concavity. These may be the points at which f’’(x) DNE or at which f’’(x) = 0. The x coordinates for the points of inflection for the graph of y = f(x) are x = -1 and x = -4. (In this example
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