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Math Help - calculus/derivative question

  1. #1
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    calculus/derivative question

    for what values of a and b is the line 2x+y=b tangent to the curve at y=ax^2 at x=-4

    help would be welcome, thanks in advnace

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  2. #2
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    Quote Originally Posted by sxusteven View Post
    for what values of a and b is the line 2x+y=b tangent to the curve at y=ax^2 at x=-4

    help would be welcome, thanks in advnace
    At x = -4 the gradient of the tangent is to the curve is -8a. So your line has to have this gradient ......

    Also, at x = -4, y = 16a. So the point (-4, 16a) lies on the curve and hence must also lie on the line .....
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by sxusteven View Post
    for what values of a and b is the line 2x+y=b tangent to the curve at y=ax^2 at x=-4

    help would be welcome, thanks in advnace

    Rewrite the equation of the line as y=-2x+b

    The slope of this line is -2

    Now, differentiate the function y=ax^2to get y'=2ax

    At x=-4, the value of the derivative is -8a.

    Now when is -2=-8a?

    Once you have a, then plug the point x=-4 into the function y=ax^2 to find the value of the function at this point [which I will call y_0].

    Then, take this point and plug it into the equation for the line:

    (y_0)=-2(-4)+b, where (-4,y_0) is the point on the function (and on the line)

    Then solve for b.

    Can you take it from here?

    --Chris
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