# Mean-value theorem question

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.

## Answers and Replies

shmoe
Science Advisor
Homework Helper
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
Science Advisor
Homework Helper
2020 Award
this is just a restatement of the MVT