Posted by Mishaka on Saturday, November 19, 2011 at 4:29pm.
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.

Calculus  Mishaka, Saturday, November 19, 2011 at 6:25pm
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

Calculus  Steve, Saturday, November 19, 2011 at 6:29pm
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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