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Math Help - i need some quick help here...

  1. #1
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    i need some quick help here...

    A cubic polynomial with a local maximum at x = 1, a local minimum at x = 3, a y-intercept of 6, and an x3 term whose coefficient is 1.

    ok, so how the flip do i do this bad johnny...thanks for any help..

    mathaction
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mathaction View Post
    A cubic polynomial with a local maximum at x = 1, a local minimum at x = 3, a y-intercept of 6, and an x3 term whose coefficient is 1.

    ok, so how the flip do i do this bad johnny...thanks for any help..

    mathaction
    Ok...i assume you want to find the cubic.

    Let the general form of the cubic be f(x) = x^3 + ax^2 + bx + c

    we know that c = 6 since this is the y-intercept.

    so we have: f(x) = x^3 + ax^2 + bx + 6

    since the local max is at x = 1, it means f'(1) = 0 and f''(1) < 0

    since the local min is at x = 3, it means f'(3) = 0 and f''(3) > 0

    can you continue? (you may not need the second derivative, i just gave you extra information for your general edification)
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