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Math Help - maximum and minimum of functions

  1. #1
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    maximum and minimum of functions

    Is there a mistake?

    y=x^3-6x^2+9x


    y'=3x^2-12x+9

    y'=0

    x=3 and x=1

    Extreme local:
    P(1,4) ---> Point maximum

    P(3,0) --->
    Point minimum

    y''=6x-12

    Point of inflection:
    P(2,2)





    Sorry. Is there any way to put graphic here?
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  2. #2
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    Quote Originally Posted by Apprentice123 View Post
    Is there a mistake?

    y=x^3-6x^2+9x


    y'=3x^2-12x+9

    y'=0

    x=3 and x=1

    Extreme local:
    P(1,4) ---> Point maximum

    P(3,0) --->
    Point minimum

    y''=6x-12

    Point of inflection:
    P(2,2)





    Sorry. Is there any way to put graphic here?
    Yes, it's all correct.

    (To put graphic, click on 'Manage Attachments' (browse and attach picture) when you click advanced reply)
    Attached Thumbnails Attached Thumbnails maximum and minimum of functions-graph.jpg  
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Apprentice123 View Post
    Is there a mistake?

    y=x^3-6x^2+9x


    y'=3x^2-12x+9 Good

    y'=0 Good

    x=3 and x=1 Good

    Extreme local:
    P(1,4) ---> Point maximum Good

    P(3,0) --->
    Point minimum Good

    y''=6x-12 Good

    Point of inflection:
    P(2,2) Good





    Sorry. Is there any way to put graphic here?



    The graph of y=x^3-6x^2+9x makes this all seem reasonable:



    --Chris
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  4. #4
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    thank you
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