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Ag Bus 313 Problem Set 1 200 Points Due: 5:00 pm on 1/20/16 Dr. Hurley Directions: Please answer all items on this homework. You must show all your work. Unless otherwise stated, please simplify your answer. 1. Please expand the following problems: (10 Points) d. (c + d)4(c + d)-2 e. (2u + v)3 a. (x + y)(z + x)(y + z) b. (r + s + t)2 c. (a + b)4 2. Please simplify the following: (5 Points) a. b. c. d. e. y = f(x) = x-2x8x16x-10x-12 y = f(x) = (x-5x6)/(x9x-3x-8) y = f(x) = x-5/4x9/4 y = f(x) = (x7)-2/7 y = f(x) = (x1/4)4/3 3. Solve x2 as a function of x1: (20 Points) a. x11/3 x22/3 = 9 b. x1-1/4 x23/4 = x13/4 x2-1/4 c. 2x14/5x21/5 = 6 d. x11/2x21/4 = 5 4. Solve the following for Y2 as a function of Y1: (20 Points) a. Y13 Y22 8 b. Y13 Y23 1000 8 64 Y14 Y22 81 d. 25 100 c. Y12 Y22 100 25 25 5. Find the horizontal and vertical intercepts of the following: (10 Points) a. y = f(x) = 8x + 24 b. y = f(x) = x2 – 4x – 21 6. Using the three equations, get Y2 as a function of Y1 (Please do not represent your answer in decimals.): (20 Points) a. Y1 = 6x13/4 Y2 = 30x23/4 x1 + x2 = 51,250 b. Y1 = 360x11/4 Y2 = 90x21/4 x1 + x2 = 10,625 Page 1 of 2 Last revised: 12/29/14 7. Find the inverse of the following functions: (20 Points) b. y = f(x) = 4x2 + 8x + 20 a. y = f(x) = 5x + 15 8. Solve for Y1: (30 Points) a. b. 4Y1 (1,000,000 4Y12 ) 2 Y13 (2,720,000 Y ) 4 1 c. 1 2 1 24Y (28,000 8Y13 ) 2 3 4 3 2 d. Y15 (324,000 4Y13 ) 4 1 8 5 3 Y1 e. (51,250 * 30 2 3 f. 4 3 1 5 3 3 4 4 5 3 Y1 3 ) Y13 Y4 3 (10,625 * 90 4 14 ) 4 4 9. Find the intersection point(s) of the two functions: (15 Points) 3 1 32 1 4 60 4 29 a. y = f(x) = 5x + 10 and y = g(x) = -2x + 3 b. y = f(x) = 59 – 5x and y = g(x) = 10 + 2x c. y = f(x) = 2x2 and y = g(x) = 8x + 42 10. Using limits, find the general slope of the following: (20 Points) a. y = f(x) = -17x + 22 b. y = f(x) = 30x2 + 140x + 425 c. y = f(x1, x2) = 5x12 + 6x1x2 + 7x22 + 95 (For this problem, you need to apply the limit formula for x1 and also for x2.) 11. Please find the derivative of the following functions: (14 Points) a. b. c. d. e. f. g. y = f(x) = -17x + 22 y = f(x) = 30x2 + 140x + 42 y = f(x) = 12x3 + 10x2 + 8x + 6 y = f(x) = x3 + 3x2 + 4x1/4 + 25 y = f(x) = (x2+x+1)(4x2 + 3x + 2) (Use the Product Rule) y= f(x) = (2x2 + 4x + 2)/ (2x + 2) (Use the Quotient Rule) y= f(x) = (4x2 + 3x + 2)-4 (Use either Generalized Power Rule or the Chain Rule) 12. Take the derivative with respect to both x1 and x2: (16 Points) a. y = f(x1, x2) = 10x1 + 9x1x2 + 8x2 + 23 b. y = f(x1,x2) = 15x11/5x22/5 c. y = f(x1, x2) = 5x12 + 6x1x2 + 7x22 + 95 d. y = f(x1,x2) = x13 + 3x12x2 + 4x1x21/4 + 17 Page 2 of 2 Last revised: 12/29/14