3. For m₁ and m₂ numbers, with m₁ { Prove that the function f:R → R is continuous but not differentiable at x = 0. f(x) = = m₂, define mix + 4 m₂x + 4 if x ≤ 0 if x > 0.
3. For m₁ and m₂ numbers, with m₁ { Prove that the function f:R → R is continuous but not differentiable at x = 0. f(x) = = m₂, define mix + 4 m₂x + 4 if x ≤ 0 if x > 0.
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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Question
![**Problem Statement:**
3. For \( m_1 \) and \( m_2 \) numbers, with \( m_1 \neq m_2 \), define
\[
f(x) =
\begin{cases}
m_1 x + 4 & \text{if } x \leq 0 \\
m_2 x + 4 & \text{if } x > 0
\end{cases}
\]
**Task:**
Prove that the function \( f : \mathbb{R} \to \mathbb{R} \) is continuous but not differentiable at \( x = 0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77cfc5ac-076f-4cb7-b69f-6b7f1cfee42f%2F81b71d28-527c-468c-9794-28ed79f7a857%2Ftecw73_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
3. For \( m_1 \) and \( m_2 \) numbers, with \( m_1 \neq m_2 \), define
\[
f(x) =
\begin{cases}
m_1 x + 4 & \text{if } x \leq 0 \\
m_2 x + 4 & \text{if } x > 0
\end{cases}
\]
**Task:**
Prove that the function \( f : \mathbb{R} \to \mathbb{R} \) is continuous but not differentiable at \( x = 0 \).
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