# Thread: Mean Value Theorem Question

1. ## Mean Value Theorem Question

I am stuck on this one problem that is due in 45 minutes. If somebody could help me out I'd greatly appreciate it.

Find all numbers c that satisfy the conclusion of the Mean Value Theorem for the following function and interval.

$f(x)=4x^3+4x-9, [0,2]$

2. The conclusion in Mean Value Theorem is that exists $c\in(0,2)$ such that
$\displaystyle\frac{f(2)-f(0)}{2}=f'(c)$
That means
$\displaystyle f'(c)=20\Rightarrow 12c^2+4=20\Rightarrow c^2=\frac{4}{3}\Rightarrow c=\frac{2\sqrt{3}}{3}$

3. Originally Posted by red_dog
The conclusion in Mean Value Theorem is that exists $c\in(0,2)$ such that
$\displaystyle\frac{f(2)-f(0)}{2}=f'(c)$
That means
$\displaystyle f'(c)=20\Rightarrow 12c^2+4=20\Rightarrow c^2=\frac{4}{3}\Rightarrow c=\frac{2\sqrt{3}}{3}$
Thank you for the fast reply. We enter our homework online, and I did that exact same work. However, for whatever reason, the computer thought the square root of 4/3 was incorrect. Your answer it took, though. Thanks again.

4. Originally Posted by Geist
Thank you for the fast reply. We enter our homework online, and I did that exact same work. However, for whatever reason, the computer thought the square root of 4/3 was incorrect. Your answer it took, though. Thanks again.
Probably because $\sqrt{\frac{4}{3}}$ is not considered to be fully simplified, both because of the $\sqrt{4}$ and the radical in the denominator.

-Dan