Originally Posted by

**hazecraze** **Question: Verify that the function satisfies the hypotheses of The Mean Value Theorem on the given interval and find all c that satisfy the conclusion of the MTV.**

$\displaystyle f(x)= \frac{x}{x+2}$, [1,4]

---

-continuous and differentiable

f(1)=1/3

f(4)=2/3

$\displaystyle \frac{2/3-1/3}{4-1}$

$\displaystyle \frac{1/3}{3}$

=1/9

$\displaystyle

f'=\frac{(x+2) -x}{(x+2)^2}

$

$\displaystyle

f'=\frac{(2)}{(x+2)^2}

$=1/9

=$\displaystyle (x+2)^2=18$

=$\displaystyle (x^2+4x-14)$

Did I make a mistake or am I suppose to use the quadratic formula to get c?