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Let I be and interval and let f : I →R and g : I → R be functions differentiable at c. If h : I → R is defined by: h(x) : = f(x)g(x) and h'(c)=f(c)g'(c)+f'(c)g(c): Prove that f(x)g(x) - f(c)g(c) = f(x)(g(x) - g(c)) + g(c)(f(x - f(c)).

Let I be and interval and let f : I →R and g : I → R be functions differentiable at c. If h : I → R is defined by: h(x) : = f(x)g(x) and h'(c)=f(c)g'(c)+f'(c)g(c): Prove that f(x)g(x) - f(c)g(c) = f(x)(g(x) - g(c)) + g(c)(f(x - f(c)).

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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Let I be and interval and let f : I →R and g : I → R be functions differentiable at c.

If h : I → R is defined by: h(x) : = f(x)g(x) and h'(c)=f(c)g'(c)+f'(c)g(c):

Prove that f(x)g(x) - f(c)g(c) = f(x)(g(x) - g(c)) + g(c)(f(x - f(c)).
 
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