# Homework Help: Mean Value Theorem

1. May 5, 2013

1. The problem statement, all variables and given/known data

State the Mean Value Theorem and find a point which satisfies the conclusions of the Mean Value Theorem for f(x)=(x-1)3 on the interval [1,4].

2. The attempt at a solution

Mean Value Theorem:states that there exists a c∈(a,b) such that f'(c)=$\frac{f(b)-f(a)}{b-a}$

3(x-1)2=$\frac{27-0}{4-1}$

3(x-1)2=$\frac{27}{3}$

3(x-1)2=9

→(x-1)2=3

→x=1±√3

∴x=1+√3 which lies on the interval [1,4].

I was wondering if I did the question correctly and if there was anything further I should add.

Last edited: May 5, 2013
2. May 5, 2013

### voko

This is all good. Almost. You need to state certain conditions for f(x) and verify that the given f(x) meets them.

3. May 5, 2013