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Thread: Concave Down and Increasing?

  1. #1

    Concave Down and Increasing?

    On which interval is the graph of f(x)=4x^(3/2) - 3x^2 both concave down and increasing?
    A. (0,1) B. (0, .5) C. (0, .25) D. (.25, .5) E. (.25, 1)

    I found f'(x)=6x^1/2 - 6x
    and f''(x)=3x^-1/2 - 6

    I set f'' equal to zero and got x=.25
    Also, I believe it is undefined at 0?

    Would the answer be C? I'm not sure where to go from here if it's not.

  2. #2
    Elite Member
    Join Date
    Jan 2012
    A function, f, is increasing as long as f' is positive and is concave down where f'' is negative.
    You want an interval where [tex]6x^{1/2}- 6x> 0[/tex] and [tex]3x^{-1/2}- 6< 0[/tex].
    Last edited by HallsofIvy; 10-15-2014 at 08:01 PM.

  3. #3
    The answer is (0, .25), correct?

    f' is positive below 1 and f'' is negative below .25, so they both overlap in (0, .25)

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