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32 (Rolle's theorem backward) Suppose f'(c) = 0. Are there necessarily two points around c where f(a) = S(b)?

32 (Rolle's theorem backward) Suppose f'(c) = 0. Are there necessarily two points around c where f(a) = S(b)?

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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32. **(Rolle's theorem backward)** Suppose \( f'(c) = 0 \). Are there necessarily two points around \( c \) where \( f(a) = f(b) \)?
Transcribed Image Text:32. **(Rolle's theorem backward)** Suppose \( f'(c) = 0 \). Are there necessarily two points around \( c \) where \( f(a) = f(b) \)?
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