16. Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves statement. (a) If f'(c) = 0, then f has a local maximum or minimum at c. (b) If f is continuous on (a, b), then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in (a, b). (c) f is differentiable and f(-2) = f(2), then there is a number c such that [c] <2 and f'(c) = 0.

16. Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves statement. (a) If f'(c) = 0, then f has a local maximum or minimum at c. (b) If f is continuous on (a, b), then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in (a, b). (c) f is differentiable and f(-2) = f(2), then there is a number c such that [c] <2 and f'(c) = 0.

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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