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Suppose that f is a differentiable function on R¹ with a period of 2.7. That is, f(x) = f(x + 2x) for all x € R¹. Find the smallest positive integer n such that f has at least n critical points on the interval (0, 4x). You answer cannot be only true for specific examples. Your answer must be true for the general situation. Hint: consider Rolle's theorem

Suppose that f is a differentiable function on R¹ with a period of 2.7. That is, f(x) = f(x + 2x) for all x € R¹. Find the smallest positive integer n such that f has at least n critical points on the interval (0, 4x). You answer cannot be only true for specific examples. Your answer must be true for the general situation. Hint: consider Rolle's theorem

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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Suppose that f is a differentiable function on R¹ with a period of 2.7. That is, f(x) = f(x + 2x) for all x € R¹. Find the smallest positive integer n such that f has at least n critical points on the interval (0, 4x). You answer cannot be only true for specific examples. Your answer must be true for the general situation. Hint: consider Rolle's theorem
Transcribed Image Text:Suppose that f is a differentiable function on R¹ with a period of 2.7. That is, f(x) = f(x + 2x) for all x € R¹. Find the smallest positive integer n such that f has at least n critical points on the interval (0, 4x). You answer cannot be only true for specific examples. Your answer must be true for the general situation. Hint: consider Rolle's theorem
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