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Math Help - find a and b given point of inflection and local min.

  1. #1
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    Exclamation find a and b given point of inflection and local min.

    The function f(x) = x^3 + ax˛ + bx has a local minimum at x=3 and a point of inflection at x = -1. Find the values of a and b.

    I don't even know where to begin on this problem; any help is appreciated.
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  2. #2
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    Quote Originally Posted by h4hv4hd4si4n View Post
    The function f(x) = x^3 + ax˛ + bx has a local minimum at x=3 and a point of inflection at x = -1. Find the values of a and b.

    I don't even know where to begin on this problem; any help is appreciated.
    The condition for an extremal point is f'(x) = 0 and the condition for a point of inflection is f''(x) = 0

    f(x) = x^3+ax^2+bx

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

    f''(x)=6x+2a

    Plug in the values you know:

    f'(3) = 0 = 27+6a+b

    f''(-1)=0= -6+2a

    Solve this system of simultaneous equations for a and b.
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  3. #3
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    I got a = 3 and b = -45

    is that correct?
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  4. #4
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    Quote Originally Posted by h4hv4hd4si4n View Post
    I got a = 3 and b = -45

    is that correct?
    I've got the same result.
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  5. #5
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    thanks for your help
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