Calculus

Suppose you know that f(x) is an odd functon on the domain of all real numbers and that the function is concave up on the intervals 0 < x < 3 and 5 < x and concave down on the interval 3 < x < 5.
List ALL intervals on which the functon f(x) is concave up and ALL intervals on which the function f(x) is concave down.

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  1. Nevermind, I figured it out. Since the function is odd it must be symmetric about the origin, so:
    concave up: -5 < x < -3 and 0 < x < 3 and x > 5
    concave down: x < -5 and -3 < x < 0 and 3 < x < 5

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  2. We don't really know anything about f(x) for x>5, but let's assume it stays concave down.

    Since f is odd, it is radially symmetric about the origin.

    So, f is concave down on -3 < x < 0
    and f is concave up on -5 < x < -3

    We will assume it stays concave up for x < -5.

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