Originally Posted by

**obsmith08** Here's the problem:

The value c that satisfies the conclusion of the Mean Value Thm for the function x/(x+2) on the interval [1,4] is:

A) 2

B) -2 + 3sq rt(2)

C) no such c exists

D) -2 + 2sq rt(6)

First, I know to find the derivative: 2c + 2/(c+2)^2 (**)

Then, I find f(b) - f(a)/(b-a) which equals 1/9

Then, I set 1/9 or f'(c) equal to the derivative which is 2c + 2/(c+2)^2

so, I end up with 2c + 2/(c^2 + 4c + 4) = 1/9

If I have done all of this correct up until this point, my only problem really lies within the algebra to solve for c in the above equation. Can anyone please help? (Would be great if someone could show me the algebra steps to find c) Thanks!