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Math Help - differentiation

  1. #1
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    Exclamation differentiation

    the tangent to the curve y= ax^2 + bx 2 at (1,1/2) is parallel to the normal to the curve y= x^2 +6x +10 at (-2,2). find the values of a and b
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by deadmotor View Post
    the tangent to the curve y= ax^2 + bx 2 at (1,1/2) is parallel to the normal to the curve y= x^2 +6x +10 at (-2,2). find the values of a and b
    How much progress have you made with this question?

    Find the slope of y= x^2 +6x +10 at (-2,2):

    y' = 2x + 1 so slope is -3
    The normal line will have slope 1/3 (negative reciprocal).

    So the slope to ax^2 + bx +? 2 at (1, 1/2) is 1/3.

    Plug in the point (1, 1/2) into the function to get one condition on a and b.
    Plug in the point x=1 and m=1/3 into the derivative of the curve.

    Then solve for a and b.

    Good luck!!
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