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November 27th, 2015, 10:55 AM   #1
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Shapes of graphs

How do I find the concavity of this function and its inflection points just by looking at it ?
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November 27th, 2015, 12:11 PM   #2
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The function is convex wherever the graph opens upwards. For example, the part of the graph nearest the $x$-axis is convex.

Likewise, the function is concave wherever the graph opens downwards. For example, in the area in the middle.

Inflection points are points where the graph switches from convex to concave (or vice versa). The first of these appears at what looks like the point (2, 5).
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November 27th, 2015, 01:05 PM   #3
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