Some help on this following question, please. Thanks a bunch!

Question: If is Riemann integrable on and continuous at , prove that is differentiable at and . Show that if has a jump discontinuity at , then is not differentiable at .

- Apr 22nd 2009, 01:34 PMLast_SingularityIf f is Riemann integrable and continuous, prove that F is differentiable
Some help on this following question, please. Thanks a bunch!

Question: If is Riemann integrable on and continuous at , prove that is differentiable at and . Show that if has a jump discontinuity at , then is not differentiable at . - Apr 22nd 2009, 02:41 PMPlato
I sure that you mean .

Notice that and the length of that interval is . - Apr 22nd 2009, 02:58 PMmanjohn12
Consider the difference quotient: .

Then you need to show that .

Use the fact that . Also use the fact that provided that is Riemann integrable. You have to consider two cases: and .