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Math Help - Where is f(x) concave and convex?

  1. #1
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    Where is f(x) concave and convex?

    Hello!

    I have this function f(x)=1,2x^5-4x^3 and I need to give the intervals where the function's graph is concave and convex.

    I know f'(x)=0 when x=\sqrt{2}, x=-\sqrt{2} and x=0

    Thanks in advance!
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  2. #2
    Member eXist's Avatar
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    From what I understand of concave and convex is as follows:

    Concave: Points on a graph where the slope is decreasing.
    Convex: Points on a graph where the slope is increasing.

    This of course is a just a simple explanation, like I said, from what I understand.

    So I'd say your looking for all the points where:
    f''(x) > 0 These would be the convex set.
    f''(x) < 0 These would be the concave set.
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  3. #3
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    f''(x) = 24x^3 - 24x = 24x(x^2-1) \Rightarrow f''(x) = 0 at x=0, x=1, x=-1

    f''(2) = 24(8-2) and f''(-2) = 24(2-8) , and f(x) is continuous in \mathbb{R} so:

    f(x) is concave at:  x > 1 ,  -1 < x < 0 and convex at:  x < -1 , 0<x<1

    Woops, late :X
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