Let f and g be continuous functions on (a, b] and differentiable at every point in the interior, with g(a) # g(b). Prove that there Chapter 5 Differential Calculus exists a point xo in (a, b) such that f(b) – f(a) _ f'(xo) g(b) – 9(a) gʻ(x0)'

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Let f and g be continuous functions on (a, b] and differentiable
at every point in the interior, with g(a) # g(b). Prove that there
Chapter 5
Differential Calculus
exists a point xo in (a, b) such that
f(b) – f(a)
f'(x0)
g(b) – g(a) ¯ gʻ(xo)
(Hint: apply the mean value theorem to the function
(S(b) – f(a))g(x) – (g(b) – g(a))f(x).)
Transcribed Image Text:Let f and g be continuous functions on (a, b] and differentiable at every point in the interior, with g(a) # g(b). Prove that there Chapter 5 Differential Calculus exists a point xo in (a, b) such that f(b) – f(a) f'(x0) g(b) – g(a) ¯ gʻ(xo) (Hint: apply the mean value theorem to the function (S(b) – f(a))g(x) – (g(b) – g(a))f(x).)
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