Determine whether Mean Value Theorem can be applied to the function on the given interval; if so, find the value(s) of c guaranteed by the theorem. (Enter your answers as a comma-separated list. )

f(x) = x + 1/x on [1, 3]

Question

Determine whether Mean Value Theorem can be applied to the function on the given interval; if so, find the value(s) of c guaranteed by the theorem. (Enter your answers as a comma-separated list. )
 
f(x) = x + 1/x on [1, 3]

anonymous · Answer

yes it is continuous and yes it is differentiable on that interval , so go ahead and find $\frac{f(3)-f(1)}{3-1}$

anonymous · Answer

4/6

anonymous · Answer

$f(1)=2,f(3)=\frac{10}{3}, f(3)-f(1)=\frac{10}{3}-1=\frac{7}{3}$

anonymous · Answer

oops yes you are right and i am wrong

anonymous · Answer

$\frac{10}{3}-2=\frac{4}{3}$ divide by 2 get $\frac{2}{3}$ 
take the derivative, set it equal to $\frac{2}{3}$ and solve for $x$

anonymous · Answer

i.e. $1-\frac{1}{x^2}=\frac{2}{3}$ etc

anonymous · Answer

yes

anonymous · Answer

but there's more to the problem