Concavity TestThe graph of a twice-differentiable function is(a) Concave up on any interval where .(b) Concave down on any interval where .A point where the graph of a function has a tangentline and where the concavity changes is a point ofinflection.yfxyyyfx0y0y
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Let’s work through #8 on p.204CP:IP:IntervalsSign of Sign of Behavior ofx< 00 < x< 11 < x< 22 < x–++++–––DecConc upIncConc upIncConc downDecConc downEstablish some graphical support!!!32263yxx2612yxx62x x0,2x1212yx121x1xyyy
Let’s work through #8 on p.204(a) Increasing on(b) Decreasing on(c) Concave up on(d) Concave up on(e) Local maximum of 5 at Local minimum of –3 at (f) Inflection point 32263yxx0,2,0 , 2, ,1 1,2x0x1,1
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