Find the number c that satisfies the conclusion of the Mean Value Theorem.

Question

f(x)=x/(x+2)

[1,4]

Answer 1

f'(c)=(f(4)-f(1))/(4-1)
f(4)=4/6=2/3
f(1)=1/3
f'(c)=1/9
f'(x)=(x+2-x)/(x+2)^2
2/(c+2)^2=1/9
(c+2)^2=18
c+2=3*sqrt(2)