Use the Mean Value Theorem to find the value of ‘c’ for the function f(x)= x^2/x+2 in [1, 2]. thanks :)

Question

Use the Mean Value Theorem to find the value of ‘c’ for the function f(x)= x^2/x+2  in [1, 2]. thanks :)

anonymous · Answer

$$f(x)=\frac{x^2}{x+2}$$
$$f(2)=1$$
$$f(1)=\frac{1}{3}$$ 
$$\frac{1-\frac{1}{3}}{2-1}=\frac{2}{3}$$

anonymous · Answer

$$f'(x)=\frac{x(x+4)}{(x+2)^2}$$ 

$$\frac{x(x+4)}{(x+2)^2}=\frac{2}{3}$$
$$3x(x+4)=2(x+2)^2$$

anonymous · Answer

now i guess we have to solve this quadratic for x.   hope i can to it

anonymous · Answer

lmaooo :P

anonymous · Answer

$$3x^2+12x=2x^2+8x+8$$
$$x^2+4x=8$$
$$(x+2)^2=8+4=12$$
$$x+2=\pm\sqrt{12}$$
$$x=-2\pm2\sqrt{3}$$

anonymous · Answer

only answer in our interval is 
$$-2+2\sqrt{3}$$

anonymous · Answer

but...

anonymous · Answer

it says the answer is between 1 and 2 :/ I dont get it :(