Hi, I want to show that this function satisfies the Mean Value Thereom however, I am stuck when I try to obtain c. The function is f (x) = x/(x+2) on the interval [1,4].

So far I have:

That because it is a rational fuction, f is continuous on [a,b] and differentiable on (a,b).

f(4) - f(1) = f'(c)(4-1)

1/3 = f ' (c)*3

f '(c) = 1/9

f'(x) = 2/[(x+2)^2]

however when i try to set f'(x) = 1/9, i do not obtain a value within [1,4]

Thank you so much for your help!