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Math Help - find constants

  1. #1
    Senior Member euclid2's Avatar
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    find constants

    find constants a,b, and c such that the graph of f(x)=x^3+ax^2+bx+c will increase to the point (-3,18), decrease to the point (1,-14) and then continue increasing
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  2. #2
    Super Member Deadstar's Avatar
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    Quote Originally Posted by euclid2 View Post
    find constants a,b, and c such that the graph of f(x)=x^3+ax^2+bx+c will increase to the point (-3,18), decrease to the point (1,-14) and then continue increasing
    Find the derivative.

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

    Set this equal to zero at the points x=-3 and x=1 which will be our critical points.

    We get 27 - 6a + b = 0 and 3 + 2a + b = 0

    Solving these simultaneous equations gives us...

    a = 3 and b = -9.

    You can check the second derivative to see that the points (-3,18) and (1,-14) are indeed a max and a min.

    Hence we have f(x) = x^3 + 3x^2 - 9x + c.

    Now just find a value of c that solves...

    -14 = 1 + 3 - 9 + c (for the point (1,-14)...)

    Graph of said function below after you find the c value...
    Attached Thumbnails Attached Thumbnails find constants-untitled.jpg  
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