University:
Glendale Community College
Course:
MAT155 | College Algebra/Functions with Review
Academic year:

2019
Views:

129

Pages:

13
Author:

Bobby Dillon

Section 3.1 Increasing and Decreasing functions and Relative Maxima and Minima (Minimum Homework: 1 – 11 odds 13, 17, 21, 25) 1) a) interval(s) where the graph is increasing. (−∞, −2) ∪ (2, ∞) b) interval(s) where the graph is decreasing. (−2,2) c) the coordinates of relative maximum point if any (−2,8) d) the relative maximum value 𝑦 = 8 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = −2 e) the coordinates of the relative minimum point if any (2, −8) f) the relative minimum value 𝑦 = −8 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = 2 3) a) interval(s) where the graph is increasing. (−2,2) b) interval(s) where the graph is decreasing. (−∞, −2) ∪ (2, ∞) c) the coordinates of relative maximum point if any (2,35) d) the relative maximum value 𝑦 = 35 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = 2 e) the coordinates of the relative minimum point if any (−2, −29) f) the relative minimum value 𝑦 = −29 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = −2 5) a) interval(s) where the graph is increasing. (−2,1) ∪ (0, ∞) b) interval(s) where the graph is decreasing. (−∞, −2) ∪ (−1,0) c) the coordinates of relative maximum point if any (−1,2) d) the relative maximum value 𝑦 = 2 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = −1 e) the coordinates of the relative minimum point if any (−2,1) 𝑎𝑛𝑑 (0,1) f) the relative minimum value 𝑦 = 1 𝑤ℎ𝑒𝑛 𝑥 = −2 ,0 7) a) interval(s) where the graph is increasing. (−3, ∞) b) interval(s) where the graph is decreasing. (−∞, −3) c) the coordinates of relative maximum point if any 𝑛𝑜𝑛𝑒 d) the relative maximum value 𝑛𝑜𝑛𝑒 e) the coordinates of the relative minimum point if any (−3,5) f) the relative minimum value 𝑦 = 5 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = −3 9) a) interval(s) where the graph is increasing. (−∞, −3) b) interval(s) where the graph is decreasing. (−3, ∞) c) the coordinates of relative maximum point if any (−3,5) d) the relative maximum value 𝑦 = 5 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = −3 e) the coordinates of the relative minimum point if any 𝑛𝑜𝑛𝑒 f) the relative minimum value 𝑛𝑜𝑛𝑒 11) a) interval(s) where the graph is increasing. (−∞, −7) ∪ (−7, −3) b) interval(s) where the graph is decreasing. (−3,1) ∪ (1, ∞) c) the coordinates of relative maximum point if any (−3, 3.7) d) the relative maximum value 𝑦 = 3.7 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = −3 e) the coordinates of the relative minimum point if any 𝑛𝑜𝑛𝑒 f) the relative minimum value 𝑛𝑜𝑛𝑒 (Minimum Homework: 1 – 11 odds 13, 17, 21, 25) #13 – 26: For each function find the following: 13) 𝑓(𝑥) = 𝑥 2 − 6𝑥 + 3 a) f’(x) 𝑓 ′ (𝑥) = 2𝑥 − 6 b) the critical numbers 𝑥 = 3 c) interval(s) where the graph is increasing. (3, ∞) d) interval(s) where the graph is decreasing. (−∞, 3) e) the coordinates of relative maximum point if any 𝑛𝑜𝑛𝑒 f) the relative maximum value 𝑛𝑜𝑛𝑒 g) the coordinates of the relative minimum point if any (3, −6) h) the relative minimum value 𝑦 = −6 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = 3 15) 𝑓(𝑥) = 𝑥 2 − 3 a) f’(x) 𝑓 ′ (𝑥) = 2𝑥 b) the critical numbers 𝑥 = 0 c) interval(s) where the graph is increasing. (0, ∞) d) interval(s) where the graph is decreasing. (−∞, 0) e) the coordinates of relative maximum point if any 𝑛𝑜𝑛𝑒 f) the relative maximum value 𝑛𝑜𝑛𝑒 g) the coordinates of the relative minimum point if any (0, −3) h) the relative minimum value 𝑦 = −3 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = 0 17) 𝑓(𝑥) = 𝑥 3 − 12𝑥 + 4 a) f’(x) 𝑓 ′ (𝑥) = 3𝑥 2 − 12 b) the critical numbers 𝑥 = 2, −2 c) interval(s) where the graph is increasing. (−∞, −2) ∪ (2, ∞) d) interval(s) where the graph is decreasing. (−2,2) e) the coordinates of relative maximum point if any (−2, 20) f) the relative maximum value 𝑦 = 20 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = −2 g) the coordinates of the relative minimum point if any (−2, −12) h) the relative minimum value 𝑦 = −12 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = −2 19) 𝑓(𝑥) = −𝑥 3 − 3𝑥 2 + 45𝑥 − 5 a) f’(x) 𝑓 ′ (𝑥) = −3𝑥 2 − 6𝑥 + 45 b) the critical numbers 𝑥 = −5, 3 c) interval(s) where the graph is increasing. (−5,3) d) interval(s) where the graph is decreasing. (−∞, −5) ∪ (3, ∞) e) the coordinates of relative maximum point if any (3,76) f) the relative maximum value 𝑦 = 76 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = 3 g) the coordinates of the relative minimum point if any (−5, −180) h) the relative minimum value 𝑦 = −180 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = −5 𝑥+2 21) 𝑓(𝑥) = 𝑥−5 −7 a) f’(x) 𝑓 ′ (𝑥) = (𝑥−5)2 b) the critical numbers 𝑥 = 5 c) interval(s) where the graph is increasing. never d) interval(s) where the graph is decreasing. (−∞, 5) ∪ (5, ∞) e) the coordinates of relative maximum point if any none f) the relative maximum value none g) the coordinates of the relative minimum point if any none h) the relative minimum value none 𝑥−4 23) 𝑓(𝑥) = 𝑥+1 5 a) f’(x) 𝑓 ′ (𝑥) = (𝑥+1)2 b) the critical numbers 𝑥 = −1 c) interval(s) where the graph is increasing. never d) interval(s) where the graph is decreasing. (−∞, −1) ∪ (−1, ∞) e) the coordinates of relative maximum point if any none f) the relative maximum value none g) the coordinates of the relative minimum point if any none h) the relative minimum value none 25) 𝑓(𝑥) = 𝑥𝑒 3𝑥 a) f’(x) 𝑓 ′ (𝑥) = 𝑒 3𝑥 (3𝑥 + 1) b) the critical numbers 𝑥 = −1/3 1 c) interval(s) where the graph is increasing. (− 3 , ∞) 1 d) interval(s) where the graph is decreasing. (−∞, − ) 3 e) the coordinates of relative maximum point if any none f) the relative maximum value none 1 −1 g) the coordinates of the relative minimum point if any (− 3 , 3𝑒 ) 1 h) the relative minimum value 𝑦 = − 3𝑒 𝑤ℎ𝑖𝑐ℎ 𝑜𝑐𝑐𝑢𝑟𝑠 𝑤ℎ𝑒𝑛 𝑥 = −1/3