Let f:[a,b] be differentiable and suppose f' is integrable on [a,b],
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.
Real Analysis question watch
- Thread Starter
- 03-12-2014 21:29
(Original post by physics94)
- 03-12-2014 22:11
[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].