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

2020
Views:

163

Pages:

2
Author:

Maliyah Hahn

Chapter 4 – Handout 2 1) Find the absolute maximum and absolute minimum 1a) 1b) 2-5: Find the absolute maximum and absolute minimum of the function under the given interval. 2) 𝑓(𝑥) = 4𝑥 3 − 108𝑥 ; [0,5] 3) 𝑓(𝑥) = −3𝑥 2 + 18𝑥; [1,7] 4) 𝑓(𝑥) = 11𝑥𝑒 𝑥 ; [-4,5] 5) 𝑓(𝑥) = 2𝑒 𝑥 ; [-3,2] 2 6) A campground owner has 1000 meters of fencing. He wants to enclose a rectangular field bordering a river, with no fencing needed along the river, and let W represent the width of the field and L represent the length of the field. Make W be the side of the fence that is perpendicular to the river so that two widths and one length will need to be constructed. a) Write an equation for the length of the field b) Write an equation for the area of the field. c) Find the domain of the area equation that was created in part b. (This domain will be of the form: # ≤ 𝑊 ≤ #) d) Find the value of w leading to the maximum area e) Find the value of L leading to the maximum area f) Find the maximum area. 𝑑𝑦 #7-12: Use implicit differentiation to determine 𝑑𝑥 . 7) x2 + 2x = 12y 8) 5y = 5x2 - 15x 9) y2 + 3x2 = 6y + 2 10) 𝑦 2 − 𝑥 2 = 4 + 2𝑥 11) 𝑦 2 − 𝑥 2 = 4 + 2𝑦 12) 𝑦 2 − 3𝑦 = 4 + 2𝑥 2 13) Find the equation of the line tangent to the graph at the indicated point. x2 + 2x = 12y (4,2) (hint see problem #7) 14) Find the equation of the line tangent to the graph at the indicated point. 5y = 5x2 - 15x (3,0) (hint see problem #8) Answers: 1) max y = 1 when x = 1, min y = -35 when x = -5 2) max y = 34 when x = 4, min y = -15 when x = -3 3) max y = 0 when x = 0, min y = -216 when x = 3 4) max y = 55e5 when x = 5, min y = -11/e when x = -1 5) max y = 2e9 when x = -3, min y = 2 when x = 0 6a) L = 1000 – 2W 6b) A = 1000W – 2W2 6c) 0 ≤ 𝑊 ≤ 500 6d) W = 250 M 6e) L = 500 M 6f) A = 125000 M2 𝑑𝑦 𝑥+1 = 6 𝑑𝑥 𝑑𝑦 𝑥 11) 𝑑𝑥 = 𝑦−1 7) 𝑑𝑦 = 2𝑥 − 3 𝑑𝑥 𝑑𝑦 4𝑥 12) 𝑑𝑥 = 2𝑦−3 8) 9) 𝑑𝑦 𝑑𝑥 −3𝑥 = 𝑦−3 10) 5 4 𝑑𝑦 𝑑𝑥 = 𝑥+1 𝑦 13) 𝑦 = 6 𝑥 − 3 14) y = 3x – 9

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