Concavity Test The graph of a twice differentiable function is a Concave up on

Concavity test the graph of a twice differentiable

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Concavity Test The 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 tangent line and where the concavity changes is a point of inflection . y f x y y y f x 0 y  0 y 
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Let’s work through #8 on p.204 CP: IP: Intervals Sign of Sign of Behavior of x < 0 0 < x < 1 1 < x < 2 2 < x + + + + Dec Conc up Inc Conc up Inc Conc down Dec Conc down Establish some graphical support!!! 3 2 2 6 3 y x x  2 6 12 y x x  6 2 x x  0,2 x 12 12 y x   12 1 x  1 x y y  y
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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 3 2 2 6 3 y x x  0,2 ,0 , 2,   ,1   1, 2 x 0 x 1,1
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