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Math Help - Family of Functions!!

  1. #1
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    Family of Functions!!

    Find a formula for the following function.
    A cubic polynomial with a local maximum at x = 7, a local minimum at x = 9, a y-intercept of 4, and an x^3 term whose coefficient is 1.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by mathlete View Post
    Find a formula for the following function.
    A cubic polynomial with a local maximum at x = 7, a local minimum at x = 9, a y-intercept of 4, and an x^3 term whose coefficient is 1.
    from the given info we know that the function looks like

    f(x)=x^3+ax^2+bx+4 so taking the derivative we get

    f'(x)=3x^2+2ax+b

    max and min points occur when the dervitive is zero so

    f'(7)=0=147+14a+b and f'(9)=0=243+18a+b

    Solving this system for a and b gives us the polynomial

    we get a=-24 \mbox{ and } b=189


    So we get f(x)=x^3-24x^2+189x+4

    I hope this helps

    Good luck
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