f(x) = x / (x+1), in the interval (1,2).... use mean value theorem to find all (c) in the interval?

Question

mean value theorum formula

f*(c) = (f(b)-f(a)) / b-a

Answer 1

f(x) = x / (x+1)
f'(x) = 1 / (x+1)^2
f(2) = 2/3
f(1) = 1/2
1/(c + 1)^2 = 1/6
c^2 + 2c + 1 = 6
c^2 + 2c - 5 = 0
c = (- 1 ± √(1 + 5))
(- 1 - √6) lies outside the interval, so
c = (- 1 + √6) ≈ 1.449490 ≈ 1.45