Suppose that a function f is differentiable at x0 and defineg(x) = f(mx + b), where m
Chapter 2, Problem 52(choose chapter or problem)
Focus on Concepts
Suppose that a function \(f\) is differentiable at \(x_{0}\) and define \(g(x)=f(m x+b)\), where \(m\) and \(b\) are constants. Prove that if \(x_{1}\) is a point at which \(m x_{1}+b=x_{0}\), then \(g(x)\) is differentiable at \(x_{1}\) and \(g^{\prime}\left(x_{1}\right)=m f^{\prime}\left(x_{0}\right)\).
Equation Transcription:
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Text Transcription:
f
x_0
g(x)=f(mx+b)
m
b
x_1
mx_1+1=x_0
g(x)
x_1
g'(x_1)=mf'(x_0)
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