# Find the number c that satisfies the conclusion of the mean value theorem.

• Jul 21st 2010, 05:39 PM
superduper1
Find the number c that satisfies the conclusion of the mean value theorem.
f(x) = x / (x+ 4) [1,8]

I found fprime(x) to be 4/(x+4)^2
Then I used (f(b) - f(a)) / (b -a) and found that to be 7/15

I set the equation to zero to solve for c and my answer comes out wrong. (squarroot60/7)-4
PS How do I use the math syntax keys on this forum?
• Jul 21st 2010, 07:45 PM
apcalculus
Pretty sure f(b) - f(a) equals 7/15 here. When you divide by (b-a), you get 1/15.

The derivative looks good.

I hope this helps! Good luck!
• Jul 22nd 2010, 01:00 AM
HallsofIvy
Set what equation to 0? The mean value theorem says that there exist some c such that
$f'(c)= \frac{f(8)- f(1)}{8- 1}$

f(8)- f(1)= 7/15. (f(8- f(1)/(9- 1)= 1/15. You want to set $\frac{x}{x+ 4}= \frac{1}{15}$.
• Jul 22nd 2010, 06:40 PM
superduper1
2/7 ?
• Jul 23rd 2010, 12:40 AM
superduper1
still not sure what I'm doing wrong, the answer i submit is wrong :/
• Jul 23rd 2010, 03:18 AM
Ackbeet
HallsofIvy was correct up until this point:

Quote:

You want to set $\frac{x}{x+4}=\frac{1}{15}.$
You actually want to set $f'(c)=\frac{4}{(c+4)^{2}}=\frac{1}{15}.$

[EDIT]: I'm sure that was a "thought-o" on HallsofIvy's part. (Wink)
• Jul 23rd 2010, 10:37 PM
superduper1
$\sqrt{60} -4 = c$

??
• Jul 24th 2010, 03:21 AM
Ackbeet
Your answer is correct. I would show the steps of rejecting the inadmissible solution when you take the square root.

I think you're done!