Help proving by Mean value theorem

• Nov 17th 2010, 04:03 PM
gordo151091
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.

• Nov 17th 2010, 06:22 PM
pickslides
Start by writing $11x+16 = x^3-x$

What is your attempt at this problem?
• Nov 17th 2010, 07:20 PM
gordo151091
Quote:

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.

• Nov 17th 2010, 07:24 PM
Drexel28
Quote:

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.

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.