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Math Help - concavity

  1. #1
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    concavity

    Without using a calculator, find the values of x for which the graph of y=x^3 - 6x^2 is concave downward.


    Thanks
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  2. #2
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    Hello, DINOCALC09!

    It's pretty straight-foward.
    Exactly where is your difficulty?


    Find the values of x for which the graph of y\:=\:x^3 - 6x^2 is concave downward.

    First derivative: . y' \:=\:3x^2 - 6x

    Second Derivative: . y'' \:=\:6x-6

    The graph is concave down when the second derivative is negative.

    So we have: . 6x-6 \:< \:0\quad\Rightarrow\quad x \:< \:1


    The graph is concave down for x \in (-\infty,\,1)

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  3. #3
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    i believe that you messed up on the first derivative and hence the concave down part is x< 2

    am i right?
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  4. #4
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by DINOCALC09 View Post
    i believe that you messed up on the first derivative and hence the concave down part is x< 2

    am i right?
    yes you are..
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