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Math Help - max/min

  1. #1
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    max/min

    Find the values of x that give relative extrema for the function  f(x) = 3x^5 - 5x^3


    What is relative maximum and relative minimum of it?
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by Samantha View Post
    Find the values of x that give relative extrema for the function  f(x) = 3x^5 - 5x^3


    What is relative maximum and relative minimum of it?
    I might not be right because I'm not sure why it says RELATIVE maximum and minimum, but to get the maximum and minimum of a function, differentiate it and set it equal to 0.

     f(x) = 3x^5 - 5x^3

     \frac{dy}{dx} \ f(x) = 15x^4 - 15x^2 = 0

     0 = 15x^2(x^2 - 1)

    So  x = 1 \ or \ x = -1 \ or \ x = 0
    Last edited by janvdl; July 26th 2007 at 06:59 AM. Reason: Added a finishing touch :-D
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    Quote Originally Posted by Samantha View Post
    Find the values of x that give relative extrema for the function  f(x) = 3x^5 - 5x^3


    What is relative maximum and relative minimum of it?
    f'(x)=15x^2(x+1)(x-1)=0 gives the stationary points x=0,-1,1.
    Attached Thumbnails Attached Thumbnails max/min-july58.gif  
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  4. #4
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    Quote Originally Posted by janvdl View Post
    I might not be right because I'm not sure why it says RELATIVE maximum and minimum, but to get the maximum and minimum of a function, differentiate it and set it equal to 0.

     f(x) = 3x^5 - 5x^3

     \frac{dy}{dx} \ f(x) = 15x^4 - 15x^2 = 0

     0 = 15x^2(x^2 - 1)

    So  x = 1 \ or \ x = -1 \ or \ x = 0
    I don't understand =(

    Is it relative maximum: x=-1, Relative minimum: x=1?
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  5. #5
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Samantha View Post
    I don't understand =(

    Is it relative maximum: x=-1, Relative minimum: x=1?
    Set these values back into the original equation and see which is the largest and smallest
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    Quote Originally Posted by Samantha View Post
    I don't understand =(

    Is it relative maximum: x=-1, Relative minimum: x=1?
    Consider the sign of its derivative at both sides of the stationary points to determine if they are relative max (min) points.
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  7. #7
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    Quote Originally Posted by janvdl View Post
    Set these values back into the original equation and see which is the largest and smallest
    No. This does not work. Because a local max can be smaller than a local min.
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  8. #8
    Bar0n janvdl's Avatar
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    Quote Originally Posted by curvature View Post
    No. This does not work. Because a local max can be smaller than a local min.
    But we are working with the extrema aren't we?
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    Quote Originally Posted by janvdl View Post
    But we are working with the extrema aren't we?
    a relative max==local max
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  10. #10
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    Is it relative maximum: x=0; relative minima: x =+-1?
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  11. #11
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Samantha View Post
    Is it relative maximum: x=0; relative minima: x =+-1?
     x = -1 is the relative maxima.

     x = +1 is the relative minima.
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  12. #12
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    Quote Originally Posted by janvdl View Post
    Besides, it's very clear to see here that we only have absolute maximum and minimum points.
    Wrong! See the curve above. There is no absolute maximum nor absolute minimum points. Only relative or local ones.
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  13. #13
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    Quote Originally Posted by janvdl View Post
     x = -1 is the absolute maxima.

     x = +1 is the absolute minima.

    Im not sure what  x = 0 is.
    x=0 is a stationary point but not a extreme point because the sign of the derivative does not change there.
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  14. #14
    Bar0n janvdl's Avatar
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    Quote Originally Posted by curvature View Post
    Wrong! See the curve above. There is no absolute maximum nor absolute minimum points. Only relative or local ones.
    Yes, i realised that now, my apologies Curvature.

    Would you mind explaining the other method of calculating maxima and minima to me?
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  15. #15
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    So there are no maximum nor minimum?
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