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The graph of a function is shown in the...

The graph of a function is shown in the following figure.

Determine the intervals on which the function is concave up and the intervals on which it is concave down. Find the x - coordinates of any inflection points.

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The graph is concave up on ` a lt x lt b, b lt x lt c and d lt x lt e`. The graph is concave down on ` c lt x lt d`.
Note that concavity is a property of a graph on an open interval, so the endpoints are not included.
There are inflection points at x = c and x = d.
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