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Math Help - Determining Values

  1. #1
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    Determining Values

    This is a calc ab problem
    f(x)= x^3+ax^2+bx+c
    1)the graph of f has a point of inflection at (0,-2)
    2)The average(mean) value of f(x) on the closed interval [0,2] is -3

    a) determine values of a b and c
    b) determine the calue of x that satisfies the conclusion of the Mean Value Theorem for f on the closed interval [0,3]

    The first derivative is 3x^2+2ax+b
    and the second is 6x+2a
    so if you substitute 0=6(0)+2a
    a= 0
    also (0,-2) is a point so
    -2=0+0+c
    so c= -2
    How would i find the rest of the information?
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  2. #2
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    Hello,
    Quote Originally Posted by calc_help123 View Post
    This is a calc ab problem
    f(x)= x^3+ax^2+bx+c
    1)the graph of f has a point of inflection at (0,-2)
    2)The average(mean) value of f(x) on the closed interval [0,2] is -3

    a) determine values of a b and c
    b) determine the calue of x that satisfies the conclusion of the Mean Value Theorem for f on the closed interval [0,3]

    The first derivative is 3x^2+2ax+b
    and the second is 6x+2a
    so if you substitute 0=6(0)+2a
    a= 0
    also (0,-2) is a point so
    -2=0+0+c
    so c= -2
    How would i find the rest of the information?
    So now you have f(x)=x^3+bx-2
    You're left to find b.

    Use 2) :
    The average value m of a function f over an interval [a,b] is :
    m=\frac{1}{b-a} \int_a^b f(x) ~dx
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