Math Is Fun Forum

mathattack

Member

Registered: 2016-03-07

Posts: 17

Help with Mean Value Theorem Problem

Hello!

I've been trying to solve this proof, but only can provide examples, (e.g. y=2x^2).  Could someone help me with the proof?  Thanks!

Suppose f is a twice-differentiable function with f(0) = 0, f(1/2) = 1/2 and f ' (0) = 0. Prove that |f '' (x)| > or = 4 for some x in the interval [0,1/2].

zetafunc

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Registered: 2014-05-21

Posts: 2,436

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Re: Help with Mean Value Theorem Problem

First use the MVT for f on the interval [0,1/2], and get an expression for f'(c) where c is some number in [0,1/2], using your initial conditions f(0) and f(1/2). Then use the MVT again on f' to get an expression for f'', and use the triangle inequality.

mathattack

Member

Registered: 2016-03-07

Posts: 17

Re: Help with Mean Value Theorem Problem

Thanks zetafunc!

One question: in order to use MVT again on f' to get an expression for f", what value do I use for f'(1/2)?  Do I use the f'(c) value that I found? [setting up MVT using f'(0) and f'(1/2)?]

Thanks!