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  8:259:55
 Block 2  10:0211:06
 Block 3  11:131:19
 Lunch
 A  11:0611:38
 B  12:0412:35
 C  12:501:19
 Block 4  1:262:30
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 176177)
 Increasing/Decreasing Functions (page 186)
 L  #6
 M  #20
 N  #44
 O  #48
