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5. Assume that f is diff on R s.t. f(0) = 0, ƒ(1) = 1, ƒ(2) that 3x € (0,2) s.t. f'(x) = (hint: MVT and IVT for der). 1 10* = 1. Show

5. Assume that f is diff on R s.t. f(0) = 0, ƒ(1) = 1, ƒ(2) that 3x € (0,2) s.t. f'(x) = (hint: MVT and IVT for der). 1 10* = 1. Show

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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**Problem 5:** Assume that \( f \) is differentiable on \(\mathbb{R}\) such that: - \( f(0) = 0 \) - \( f(1) = 1 \) - \( f(2) = 1 \) Show that there exists \( x \in (0,2) \) such that \( f'(x) = \frac{1}{10} \). *Hint: Use the Mean Value Theorem (MVT) and the Intermediate Value Theorem (IVT) for derivatives.*
Transcribed Image Text:**Problem 5:** Assume that \( f \) is differentiable on \(\mathbb{R}\) such that: - \( f(0) = 0 \) - \( f(1) = 1 \) - \( f(2) = 1 \) Show that there exists \( x \in (0,2) \) such that \( f'(x) = \frac{1}{10} \). *Hint: Use the Mean Value Theorem (MVT) and the Intermediate Value Theorem (IVT) for derivatives.*
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