Math Help - Help proving by Mean value theorem

1. Help proving by Mean value theorem

Hey everybody. The problem goes like this.

Proof that the line y=11x+16 does not intersect the curve x^3-x in no other points different than (-2,-6) and (4,60) by Mean value theorem.

Thanks for your help

2. Start by writing $11x+16 = x^3-x$

What is your attempt at this problem?

3. Originally Posted by pickslides
Start by writing $11x+16 = x^3-x$

What is your attempt at this problem?
$$0 =\left (x+2 \right )^{2} \left ( x-4 \right )$
$

I dont know how to proof by Mean value theorem that only two points are the intersection between the line and the curve.

Thanks for your help.

4. Originally Posted by gordo151091
$$0 =\left (x+2 \right )^{2} \left ( x-4 \right )$
$

I dont know how to proof by Mean value theorem that only two points are the intersection between the line and the curve.

Thanks for your help.
Show that if $f(x)=(x+2)^2(x-4)$ had another solution then $f'(x)$ would have to equal zero somewhere on the appropriate interval.