# Thread: 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.

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

What is your attempt at this problem?

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

What is your attempt at this problem?
$\displaystyle $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.

$\displaystyle $0 =\left (x+2 \right )^{2} \left ( x-4 \right )$$
Show that if $\displaystyle f(x)=(x+2)^2(x-4)$ had another solution then $\displaystyle f'(x)$ would have to equal zero somewhere on the appropriate interval.