5. Suppose that f is a continuous function such that f(x) > 0 for all æ and f(0) = 4, 1 f'(x) > 0 if x < 0 or x > 2, and f'(x) < 0 if 0 < x < 2, f"(-1) = f"(1) = 0, f"(x) > 0 if x < -1 or x > 1, and f"(x) < 0 if –1< x < 1. (i) Can f have an absolute maximum? If so, sketch a possible graph of f. If not, explain why. (ii) Can f have an absolute minimum? If so, sketch a possible graph of f. If not, explain why. (ii) Sketch a possible graph for f that does not achieve an absolute minimum.

5. Suppose that f is a continuous function such that f(x) > 0 for all æ and f(0) = 4, 1 f'(x) > 0 if x < 0 or x > 2, and f'(x) < 0 if 0 < x < 2, f"(-1) = f"(1) = 0, f"(x) > 0 if x < -1 or x > 1, and f"(x) < 0 if –1< x < 1. (i) Can f have an absolute maximum? If so, sketch a possible graph of f. If not, explain why. (ii) Can f have an absolute minimum? If so, sketch a possible graph of f. If not, explain why. (ii) Sketch a possible graph for f that does not achieve an absolute minimum.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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