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NWeid1
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1. Homework Statement
Give a graphical argument that if f(a)=g(a) and f'(x)>g'(x) for all x>a, then f(x)>g(x) for all x>a. Use the Mean Value Theorem to prove it.
2. Homework Equations
3. The Attempt at a Solution
I have sketched a graphical argument to show that f(x)>g(x). Then I applied the MVT and got
[tex]f'(c)=\frac{f(b) - f(a)}{b - a} > g'(c)=\frac{g(b) - g(a)}{b - a}[/tex]
[tex]-f'(c)(b - a) + f(b) = f(a) > -g'(c)(b - a) + g(b) = g(a)[/tex]
But now I'm stuck and don't know how to get to f(x) > g(x).
Give a graphical argument that if f(a)=g(a) and f'(x)>g'(x) for all x>a, then f(x)>g(x) for all x>a. Use the Mean Value Theorem to prove it.
2. Homework Equations
3. The Attempt at a Solution
I have sketched a graphical argument to show that f(x)>g(x). Then I applied the MVT and got
[tex]f'(c)=\frac{f(b) - f(a)}{b - a} > g'(c)=\frac{g(b) - g(a)}{b - a}[/tex]
[tex]-f'(c)(b - a) + f(b) = f(a) > -g'(c)(b - a) + g(b) = g(a)[/tex]
But now I'm stuck and don't know how to get to f(x) > g(x).
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