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Math Help - intro derivitives application

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by jamman790 View Post
    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.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    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?
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  4. #4
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    Quote Originally Posted by jamman790 View Post
    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?
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