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Math Help - decreasing function and concavity

  1. #1
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    decreasing function and concavity

    On what intervals is the function f(x)=x3−3x 2


    decreasing and concave up

    i took the derivative and got 3x^2-6x. Then i found the zeroes which are x=0,2. I checked where the function was decreasing and i got (-infinity,1] but it keeps saying its wrong. I don't get why.
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  2. #2
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    The function is decreasing when the derivative is less than zero. Using your correct calculation of the derivative:

    3x^2 - 6x < 0

    3x(x - 2) < 0

    Now you can analyze the derivative to find out where it is negative. On what interval(s) is it negative?
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  3. #3
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    so the function is increasing when x<0, decreasing between 0 to 2, and increasing when x>2. I still don't get how to write the interval
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  4. #4
    Super Member 11rdc11's Avatar
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    (0,2) is where it is decreasing
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  5. #5
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    You said it yourself: x is between 0 and 2. This statement about an interval is commonly written as x \in (0, 2) or 0 < x < 2.
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  6. #6
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    it said (0,2) was wrong. i tried that already.
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  7. #7
    Super Member 11rdc11's Avatar
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    To find concavity use the second derivative test
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  8. #8
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by jojoferni244 View Post
    it said (0,2) was wrong. i tried that already.
    Did you try entering in the answer the way icemanfan said?
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  9. #9
    Super Member 11rdc11's Avatar
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    Try (1,2) I think that is the answer because it wants when concave up and decreasing.
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