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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'(e) = 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). (e) f is differentiable and f(-2)=f(2), then there is a number e such that lel<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'(e) = 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). (e) f is differentiable and f(-2)=f(2), then there is a number e such that lel<2 and f'(c) = 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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(e) 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 e such that lel<2 and f'(c) = 0.
Transcribed Image Text: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(e) 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 e such that lel<2 and f'(c) = 0.
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