Updates Unit 3 Test tomorrow, 10/24!
 Recording
Bell RingerLocate the absolute extrema of the function f(x) = 2x2 + 12x  4 on the closed interval [6, 6]. no absolute max; absolute min: f(6) = 140 absolute max: f(3) = 22; absolute min: f(6) = 140 absolute max: f(6) = 140; no absolute min absolute max: f(6) = 140; absolute min: f(3) = 22 no absolute max or min
Find all the relative extrema for the following function: f(x) = sin(x) + cos(x) on the interval [0, 2π]. Relative Max: (5π / 4, sqrt(2)); Relative Min: (π / 4, sqrt(2)) Relative Max: (π / 4, sqrt(2)); Relative Min: (π / 4, sqrt(2)) Relative Max: (π / 4, sqrt(2)); Relative Min: (5π / 4, sqrt(2)) Relative Max: (π / 4, sqrt(2)); Relative Min: (5π / 4, sqrt(2)) none of the above
Determine whether Mean Value Theorem can be applied to the function f(x) = x3 on the closed interval [0, 16]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (0, 16) such that f’(c) = [f(b)  f(a)] / (b  a). MVT applies; c = 4 MVT applies; c = 16sqrt(3) / 3 MVT applies; c = 8 MVT applies; c = 16sqrt(3) / 3 MVT does not apply
Find the open intervals where the function f(x) = sin(x) + cos(x) is increasing or decreasing on the closed interval [0, 2π] Increasing: (∞, π/4) and (5π/4, ∞)  Decreasing: (π/4, 5π/4) Decreasing: (∞, π/4) and (5π/4, ∞)  Increasing: (π/4, 5π/4) Increasing: (∞, π/4)  Decreasing: (π/4, 5π/4) and (5π/4, ∞) Decreasing: (∞, π/4)  Increasing: (π/4, 5π/4) and (5π/4, ∞) none of the above
Find all intervals on which f(x) = (x + 1) / (x  3) is concave downward. (1. ∞) (∞, ∞) (∞, 3) (3, ∞)  none of the above
Review Lesson Exit Ticket  Lesson Objective(s) How can derivatives be used to find optimum conditions?
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
 Concavity and Points of Inflection (page 195)
 P  #6
 Q  #16
R  #18 S  #20
 T  #24
U  #32 V  #38
 W  #52
 Limits at Infinity
 Optimization
