A twice-differentiable function f is defined for all real numbers x. The derivative of the function...
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A twice-differentiable function f is defined for all real numbers x. The derivative of the function f and its second derivative have the properties and various values of x, as indicated in the table. 0<x<3 3 3<x< 6 6 f'(x) positive DNE negative 0 f"(x) positive DNE positive 0 X 6<x<9 negative negative Part A: Find all values of x at which f has a relative extrema on the interval [0, 9]. Determine whether f has a relative maximum or a relative minimum at each of these values. Justify your answer. (10 points) Part B: Determine where the graph of f is concave up and where it is concave down. Support your answer. (10 points) Part C: Find any points of inflection of f. Show the analysis that leads to your answer. (10 points) A twice-differentiable function f is defined for all real numbers x. The derivative of the function f and its second derivative have the properties and various values of x, as indicated in the table. 0<x<3 3 3<x< 6 6 f'(x) positive DNE negative 0 f"(x) positive DNE positive 0 X 6<x<9 negative negative Part A: Find all values of x at which f has a relative extrema on the interval [0, 9]. Determine whether f has a relative maximum or a relative minimum at each of these values. Justify your answer. (10 points) Part B: Determine where the graph of f is concave up and where it is concave down. Support your answer. (10 points) Part C: Find any points of inflection of f. Show the analysis that leads to your answer. (10 points)
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To determine the relative extrema of the function f on the interval 0 9 we need to analyze the behavior of the first derivative and second derivative ... View the full answer
Related Book For
Basic Technical Mathematics
ISBN: 9780137529896
12th Edition
Authors: Allyn J. Washington, Richard Evans
Posted Date:
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