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Math Help - tangent line/derivative

  1. #1
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    tangent line/derivative

    Find the values of x for all points on the graph of f(x)= x^3 + 2x^2 + 5x -16 at which the slope of the tangent line is 5.

    my work:

    f(x)= x^3 + 2x^2 + 5x -16
    f`(x) = 3x^2 + 4x + 5
    5 = 3x^2 + 4x + 5
    0 = 3x^2 + 4x

    stuck after this...
    Last edited by algebra2; October 23rd 2008 at 06:14 PM.
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  2. #2
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    Quote Originally Posted by algebra2 View Post
    Find the values of x for all points on the graph of f(x)= x^3 + 2x^2 + 5x -16 at which the slope of the tangent line is 4.

    my work:

    f(x)= x^3 + 2x^2 + 5x -16
    f`(x) = 3x^2 + 4x + 5
    5 = 3x^2 + 4x + 5
    0 = 3x^2 + 4x

    stuck after this...
    5 = 3x^2 + 4x + 5 ??? look again at your problem statement.

    should be ...

    4 = 3x^2 + 4x + 5

    0 = 3x^2 + 4x + 1

    0 = (3x + 1)(x + 1)

    finish.



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  3. #3
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    oh sorry i typed it wrong, the slope should be 5.

    ...and how do you factor polynomials with a number in front like 3x^2 + 4x, there's a three in front of the x^2. is there a technique to this?
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  4. #4
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    first rule of factoring ... pull out whatever factors each term has in common.

    3x^2 + 4x = 0

    x(3x + 4) = 0

    x = 0

    x = -\frac{4}{3}
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  5. #5
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    i see, thank you.
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