AP Calculus November 14-15, 2016 Mrs. Agnew

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Presentation transcript:

AP Calculus November 14-15, 2016 Mrs. Agnew Curve Sketching #2 AP Calculus November 14-15, 2016 Mrs. Agnew

Essential Question Essential Vocabulary How do you sketch curves using derivatives? Essential Vocabulary Mean Value Theorem Points of INflection Concavity Sign Analysis Chart

Concavity Concave Up: f ‘(x) is increasing on the interval. Concave Down: f ’(x) is decreasing on the interval. Concave up “holds water” while concave down “does not hold water.”

Points of Inflection Points where function changes in concavity. Points of inflection are where f ′ ′(x) is equal to zero or undefined. If f ′ ′ (x) > 0, then concave up. If f ′ ′(x) < 0, then concave down.

Sign Analysis Chart Earlier, we made a sign chart to determine intervals of increase/decrease. We will make another sign chart to determine intervals where function is concave up/down. Use points of inflection to find intervals where we will test for concavity. Examples

Sketching Curves We can use the information we have discussed to sketch the graphs of functions Asymptotes, zeros, symmetry, holes Intervals of Increase/Decrease Extreme Values Inflection Points Concavity Examples

Homework Page 195 – 197 #9, 11, 15, 23, 27, 31, 35, 60, 73, 75