1. ## intro derivitives application

So im having a little trouble trying to solve this problem! any help would be great!

A speeding driver, trying to negotiate a curve y= 0.125x^2 +2, leaves the road at the point ( 2, 2.5 ), travelling in a straight line in the direction of the tangent. Unfortunately there is another curve y= ( x - 7) ^2 + 5 coming up ahead of him. At what point(s) will he his this next curve?

thanks a lot

2. Originally Posted by jamman790
So im having a little trouble trying to solve this problem! any help would be great!

A speeding driver, trying to negotiate a curve y= 0.125x^2 +2, leaves the road at the point ( 2, 2.5 ), travelling in a straight line in the direction of the tangent. Unfortunately there is another curve y= ( x - 7) ^2 + 5 coming up ahead of him. At what point(s) will he his this next curve?

thanks a lot
What is the tangent line to y= 0.125x^2+ 2 at (2, 2.5)? Where does this line intersect the graph y= (x- 7)^2+ 5.

3. Originally Posted by HallsofIvy
What is the tangent line to y= 0.125x^2+ 2 at (2, 2.5)? Where does this line intersect the graph y= (x- 7)^2+ 5.
so would it look like this? 1/4x = (x-7)^2 + 5 - 2.5/x-2?

4. Originally Posted by jamman790
so would it look like this? 1/4x = (x-7)^2 + 5 - 2.5/x-2?
No. (1/4)x is the derivative function, not the tangent line. I have no idea where you got the "-2.5/x-2". The slope of the tangent line at x= 2 is (1/4)(2)= 1/2. What is the equation of the line through (2, 2.5) with slope 1/2?