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Math Help - finding values of variables with tangent lines

  1. #1
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    need help!

    suppose the curve y=x^4+ax^3+bx^2+cx+d has a tangent line when x=o with the equation y=2x+1 and a tangent line when x=1 with the equation y=2-3x. find the values of a, b, c, d
    Last edited by pageraets; October 8th 2007 at 07:09 PM. Reason: urgent
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  2. #2
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    Quote Originally Posted by pageraets View Post
    suppose the curve y=x^4+ax^3+bx^2+cx+d has a tangent line when x=o with the equation y=2x+1 and a tangent line when x=1 with the equation y=2-3x. find the values of a, b, c, d
    Well,
    \frac{dy}{dx} = 4x^3 + 3ax^2 + 2bx + c

    We know that when x = 0 we have a tangent line with a slope of 2. So:
    2 = c

    Similarly we know that when x = 1 we have a tangent line with a slope of -3. So:
    -3 = 4 + 3a + 2b + c

    You might think we are done, but oh no! There's more:
    We also know that at the point x = 0 the tangent line shares a point with the function y, so y = 2x + 1 at x = 0 gives the point (0, 1). Thus
    y=x^4+ax^3+bx^2+cx+d \implies 1 = d

    Similarly the tangent line shares a point with the function when x = 1, so y = -3x + 2 gives the point (1, -1):
    y=x^4+ax^3+bx^2+cx+d \implies 1 = 1 -a + b -c + d

    You should be able to solve this from here.

    -Dan
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