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1. Consider the function f(x)= x-x5+ sin(27(x - 1)). Use the MVT to prove that there exists a c with 0 < c < 1 such that the tangent line to the graph of f at c is horizontal. (Hint: What is the slope of a horizontal line?)

1. Consider the function f(x)= x-x5+ sin(27(x - 1)). Use the MVT to prove that there exists a c with 0 < c < 1 such that the tangent line to the graph of f at c is horizontal. (Hint: What is the slope of a horizontal line?)

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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1. Consider the function f(x) = x - x + sin(27(x - 1)). Use the MVT to prove that there exists a c with 0 <c< 1 such that the tangent line to the graph of f at c is horizontal. (Hint: What is the slope of a horizontal line?)
Transcribed Image Text:1. Consider the function f(x) = x - x + sin(27(x - 1)). Use the MVT to prove that there exists a c with 0 <c< 1 such that the tangent line to the graph of f at c is horizontal. (Hint: What is the slope of a horizontal line?)
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