How does the mean-value theorem relate to the difference quotient?

[trap]

Use the mean-value theorem to show that if f is continuous at x and x+h and differentiable in between, then

f(x+h)-f(x) = f ' [x+ (delta) (h)] h

for some number delta between 0 and 1.

 

[shmoe]

If you apply the mean value theorem to f on the interval [x,x+h] what do you get? How does this differ from what you are after?

 

[mathwonk]

this is just a restatement of the MVT