- #1
mtayab1994
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Homework Statement
Let f and g be two continuous functions on [a,b] and differentiable on ]a,b[ such that for every x in ]a,b[ : f'(x)<g'(x)
Homework Equations
Show that f(b)-f(a)<g(b)-g(a)
The Attempt at a Solution
So I said that there exists a c in ]a,b[ such that f'(c)=(f(b)-f(a))/(b-a) and g'(c)=(g(b)-g(a))/(b-a) and since f'(x)<g'(x) then f'(c)<g'(c) and that implies that f'(c)/g'(c)<1 and when substituting in what we found we get that (f(b)-f(a))/(g(b)-g(a))<1 and that implies that f(b)-f(a)<g(b)-g(a). Is this correct??
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