8. In this problem you will construct a generalization of Rolle's Theorem.2 We will refer to the version you already know as the 1st Rolle Theorem. (a) The 2nd Rolle's Theorem states: Let a < b. Let f be a function defined on [a, b). IF (some conditions about continuity and derivatives) f(a) = f'(a) = 0 f(b) = 0 THEN 3c E (a, b) such that f"(c) = 0. %3D Complete the statement of the theorem and prove it. Hint: Use 1st Rolle Theorem on f on [a, b). Then use 1st Rolle Theorem again (where?)
8. In this problem you will construct a generalization of Rolle's Theorem.2 We will refer to the version you already know as the 1st Rolle Theorem. (a) The 2nd Rolle's Theorem states: Let a < b. Let f be a function defined on [a, b). IF (some conditions about continuity and derivatives) f(a) = f'(a) = 0 f(b) = 0 THEN 3c E (a, b) such that f"(c) = 0. %3D Complete the statement of the theorem and prove it. Hint: Use 1st Rolle Theorem on f on [a, b). Then use 1st Rolle Theorem again (where?)
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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Transcribed Image Text:8. In this problem you will construct a generalization of Rolle's Theorem.? We will
refer to the version you already know as the 1st Rolle Theorem.
(a) The 2nd Rolle's Theorem states:
Let a < b. Let f be a function defined on a, b|. IF
• (some conditions about continuity and derivatives)
f(a) = f'(a) = 0
• f(b) = 0
THEN 3c E (a, b) such that f"(c) = 0.
%3D
Complete the statement of the theorem and prove it.
Hint: Use 1st Rolle Theorem on f on [a, b). Then use 1st Rolle Theorem again
(where?)
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