Updates- Quiz 7 on Friday!
- Covers the entire new unit so far
- Extrema
- Rolle's Theorem
- Mean Value Theorem
- Increasing and Decreasing Functions
- First Derivative Test
- Concavity
- Second Derivative Test
- Today's Schedule
- Block 1 - 8:25-9:55
- Block 2 - 10:02-11:06
- Block 3 - 11:13-1:19
- Lunch
- A - 11:06-11:38
- B - 12:04-12:35
- C - 12:50-1:19
- Block 4 - 1:26-2:30
Bell Ringer
- Increasing/Decreasing Functions
Find the open intervals where the function f(x) = sin(x) + cos(x) is increasing or decreasing on the closed interval [0, 2π] Increasing: (0, π/4) and (5π/4, 2π) | Decreasing: (π/4, 5π/4) Decreasing: (0, π/4) and (5π/4, 2π) | Increasing: (π/4, 5π/4) Increasing: (0, π/4) | Decreasing: (π/4, 5π/4) and (5π/4, 2π) Decreasing: (0, π/4) | Increasing: (π/4, 5π/4) and (5π/4, 2π) none of the above
Identify the open intervals where the function f(x) = -4x2 - 6x - 4 is increasing or decreasing. Increasing: (-∞, -¾) | Decreasing: (-¾, ∞) Decreasing: (-∞, -¾) | Increasing: (-¾, ∞) Increasing on (-∞, ∞) Decreasing on (-∞, ∞) - none of the above
Review Lesson- Concavity and Inflection Points
- Second Derivative Test
- How is the concavity of a function related to its first derivative?
- How is the concavity of a function related to its second derivative?
- Checkpoints (page 195)
- P - #6
- Q - #16
R - #18
- S - #20
- T - #24
U - #32- V - #38
- W - #52
Exit Ticket- Posted on the board at the end of the class.
| Lesson Objective(s)- How can derivatives be used to find concavity?
- How can derivatives be used to find points of inflection?
Standard(s) - #1 - Make sense of problems and persevere in solving them
- #2 - Reason abstractly and quantitatively
- #5 - Use appropriate tools strategically
- #6 - Attend to precision
- #8 - Look for and express regularity in repeated reasoning
Past Checkpoints - Extrema (page 169)
- A - #4
- B - #6
- C - #18
- D - #22
- E - #34
- Rolle's Theorem (page 176)
- Mean Value Theorem (page 176-177)
- Increasing/Decreasing Functions (page 186)
- L - #6
- M - #20
- N - #44
- O - #48
|
|