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 :)

Answer 1

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

Answer 2

\[f'(x)=\frac{x(x+4)}{(x+2)^2}\]

\[\frac{x(x+4)}{(x+2)^2}=\frac{2}{3}\]
\[3x(x+4)=2(x+2)^2\]

Answer 3

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

Answer 4

lmaooo :P

Answer 5

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

Answer 6

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

Answer 7

but...

Answer 8

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