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# Real Analysis question watch

1. Let f:[a,b] be differentiable and suppose f' is integrable on [a,b],
Prove that

int(a to b) |f(x) - f^| dx < or = (b-a) int(a to b) |f'(x)|

where f^ = (1/b-a) int(a to b) f.

Anyone have any idea how to do this question, i don't even know where to start.

Thanks
2. (Original post by physics94)
..
I'm not certain this will work, but see if you can show - the result follows easily from this.

[I'm pretty sure it does work, but it's not completely trivial - one method would be to use the MVT to show we can find c with f(c) = f^ and then treat the cases a<=x<=c and c<=x<=b separately].

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Updated: December 3, 2014
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