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

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

3. 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.”

4. 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.

5. 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

6. 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

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