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Math Help - Calculus AP Question

  1. #1
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    Calculus AP Question

    Let f be defined by f(x)= x^3 + ax^2 + bx + c and having the following properties

    1) The graph of f has a point of inflection at (0,-2)
    2) the average value of f(x) on the closed interval [0,-2] is -3

    * Find the values of a, b, and c*
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  2. #2
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    Quote Originally Posted by meg24209 View Post
    Let f be defined by f(x)= x^3 + ax^2 + bx + c and having the following properties

    1) The graph of f has a point of inflection at (0,-2)
    Inflection points are found takin' the second derivative of the function and equal it to zero, can you do that?

    Quote Originally Posted by meg24209 View Post
    2) the average value of f(x) on the closed interval [0,-2] is -3
    You need to compute \frac{1}<br />
{{0 + 2}}\int_{ - 2}^0 {\left( {x^3  + ax^2  + bx + c} \right)\,dx}  =  - 3.
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