**We need you to answer this question!**

###### If you know the answer to this question, please register to join our limited beta program and start the conversation right now!

## Related Questions

###### Asked in Statistics, Calculus, Mathematicians

### What is the difference between mean value theorem of integration and Mean Value Theorem of differentiation?

The mean value theorem for differentiation guarantees the
existing of a number c in an interval (a,b) where a function f is
continuous such that the derivative at c (the instantiuous rate of
change at c) equals the average rate of change over that
interval.
mean value theorem of integration guarantees the existing of a
number c in an interval (a,b)where a function f is continuous such
that the (value of the function at c) multiplied by the length of
the interval (b-a) equals the value of a the definite integral from
a to b. In other words, it guarantees the existing of a rectangle
(whose base is the length of the interval b-a that has exactly the
same area of the region under the graph of the function f (betweeen
a and b).