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