Math 1425.P70
Section 2.3,4,5
Name _____________________________________________
9/25/2014
Solve the problem.
1) The annual revenue and cost functions
for a manufacturer of grandfather clocks are approximately
R(x) = 500x - 0.03x 2 and C(x) = 120x + 100,000, where x denotes the number of clocks made. What is the
maximum annual profit?
A) $1,303,333
B) $1,103,333
2) The annual revenue and cost functions
C) $1,203,333
D) $1,403,333
for a manufacturer of precision gauges are approximately
R(x) = 520x - 0.02x 2 and C(x) = 160x + 100,000, where x denotes the number of gauges made. What is the
maximum annual profit?
A) $1,720,000
B) $1,520,000
Section 2.3,4,5
C) $1,820,000
D) $1,620,000
Determine the vertical asymptote(s) of the given function. If none exists, state that fact.
x+4
3) g(x) =
x 2 - 49
4) R(x) =
5) R(x) =
-3x 2
x 2 + 3x - 40
x-1
x 3 + 4x 2 - 45x
Math 1425.P70 Section 2.3,4,5, page 2
Determine the horizontal asymptote of the given function. If none exists, state that fact.
3x - 8
6) h(x) =
x-7
7) h(x) = 4 -
3
x
8) h(x) =
5x 2 - 2x - 2
2x 2 - 5x + 7
9) h(x) =
4x 3 - 4x
8x 3 - 5x + 3
Math 1425.P70 Section 2.3,4,5, page 3
Graph the rational function.
7x + 1
10) f(x) =
x
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8
x
-4
-6
-8
-10
11) f(x) =
2x
x+2
12
y
8
4
-12
-8
-4
4
8
12 x
-4
-8
-12
Find the absolute maximum and absolute minimum values of the function, if they exist, over the indicated interval, and
indicate the x-values at which they occur.
12) f(x) = 7 + 2x - x 2 ; [0, 3]
10
y
8
6
4
2
1
2
3
x
Math 1425.P70 Section 2.3,4,5, page 4
13) f(x) = x 2 - 2x + 3;
10
[0, 3]
y
8
6
4
2
1
2
3
x
Solve the problem.
14) [BONUS] From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides can be
folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum
volume? Round to the nearest tenth, if necessary.
Math 1425.P70 Section 2.3,4,5, page 5
15) [BONUS] A private shipping company will accept a box for domestic shipment only if the sum of its length
and girth (distance around) does not exceed 120 in. What dimensions will give a box with a square end the
largest possible volume?
16) Find the number of units that must be produced and sold in order to yield the maximum profit, given the
following equations for revenue and cost:
R(x) = 40x - 0.5x 2
C(x) = 7x + 3.
Math 1425.P70 Section 2.3,4,5, page 6
Answer Key
Testname: 1425_SECTION2_3_4_5
1) B
2)
3)
4)
5)
6)
7)
B
x = -7, x = 7
x = -8, x = 5
x = -9, x = 0, x = 5
y=3
y=4
5
8) y =
2
9) y =
1
2
10)
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8
x
-4
-6
-8
-10
11)
y
12
8
4
-12
-8
-4
4
8
12 x
-4
-8
-12
12) Absolute maximum = 8 at x = 1; absolute minimum =
4 at x = 3
13) Absolute maximum = 6 at x = 3; absolute minimum =
2 at x = 1
14) 6.7 in. by 6.7 in. by 1.7 in.; 74.1 in. 3
15) 20 in. x 20 in. x 40 in.
16) 33 units
Math 1425.P70 Section 2.3,4,5, page 7