MATH 1329 Final Exam Review 2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers
the question.
Find the intervals of increase and decrease for the given function.
f
1) (t) =
1
1)
25 - t2
A) f (t) is increasing for t < -5 and -5 < t < 0; f (t) is decreasing for 0 < t < 5 and t >
5.
B) f (t) is increasing for 0 < t < 5 and t > 5; f (t) is decreasing for t < -5 and -5 < t <
0.
C) f (t) is increasing for 0 < t < 5; f (t) is decreasing for t < -5 and t > 5.
D) f (t) is increasing for t < -5 and t > 5; f (t) is decreasing for 0 < t < 5.
2) f (x) = x3 - 48x + 2 2)
A) f (x) is increasing for x < 24; f (x) is decreasing for x > 24.
B) f (x) is increasing for -4 < x < 4; f (x) is decreasing for x < -4 and x >
4.
C) f (x) is increasing for x > 24; f (x) is decreasing for x < 24.
D) f (x) is increasing for x < -4 and x > 4; f (x) is decreasing for -4 < x < 4.
Solve the problem.
3) The output at a certain plant is Q = 0.09x2 + 0.13xy + 0.03y2 units per day, where x is the 3)
number of hours of skilled labor used and y is the number of hours of unskilled labor
used. Currently, 70 hours of skilled labor and 200 hours of unskilled labor are used each
day. Use calculus to estimate the change in unskilled labor that should be made to offset
a 1-hour increase in skilled labor so that output will be maintained at its current level.
A) decrease unskilled labor by approximately 2.556 hours each day
B) decrease unskilled labor by approximately 4.214 hours each day
C) decrease unskilled labor by approximately 1.829 hours each day
D) decrease unskilled labor by approximately 1.531 hours each day
4) Leticia manages a company whose total weekly revenue is 4)
R(q) = 250q - 0.05q2
dollars when q units are produced and sold. Currently, the company produces and
sells 60 units a week. Using marginal analysis, Leticia estimates the additional
revenue that will be generated by the production and sale of the 61st unit. What does
she discover? Based on this result, should she recommend increasing the level of
production?
A) $225.60; yes B) $225.60; no C) $244.00; no D) $244.00;
yes
5) A company estimates that if x thousand dollars are spent on the marketing of a 4
certain product, then Q(x) thousand units of the product will be sold, where 8
Q(x) = 4x +
1
, x2 5)
For what value of x is the sales rate minimized?
A) $9500 B) $7000 C) $15,000 D) $12,000
2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers
the question.
Find the intervals of increase and decrease for the given function.
f
1) (t) =
1
1)
25 - t2
A) f (t) is increasing for t < -5 and -5 < t < 0; f (t) is decreasing for 0 < t < 5 and t >
5.
B) f (t) is increasing for 0 < t < 5 and t > 5; f (t) is decreasing for t < -5 and -5 < t <
0.
C) f (t) is increasing for 0 < t < 5; f (t) is decreasing for t < -5 and t > 5.
D) f (t) is increasing for t < -5 and t > 5; f (t) is decreasing for 0 < t < 5.
2) f (x) = x3 - 48x + 2 2)
A) f (x) is increasing for x < 24; f (x) is decreasing for x > 24.
B) f (x) is increasing for -4 < x < 4; f (x) is decreasing for x < -4 and x >
4.
C) f (x) is increasing for x > 24; f (x) is decreasing for x < 24.
D) f (x) is increasing for x < -4 and x > 4; f (x) is decreasing for -4 < x < 4.
Solve the problem.
3) The output at a certain plant is Q = 0.09x2 + 0.13xy + 0.03y2 units per day, where x is the 3)
number of hours of skilled labor used and y is the number of hours of unskilled labor
used. Currently, 70 hours of skilled labor and 200 hours of unskilled labor are used each
day. Use calculus to estimate the change in unskilled labor that should be made to offset
a 1-hour increase in skilled labor so that output will be maintained at its current level.
A) decrease unskilled labor by approximately 2.556 hours each day
B) decrease unskilled labor by approximately 4.214 hours each day
C) decrease unskilled labor by approximately 1.829 hours each day
D) decrease unskilled labor by approximately 1.531 hours each day
4) Leticia manages a company whose total weekly revenue is 4)
R(q) = 250q - 0.05q2
dollars when q units are produced and sold. Currently, the company produces and
sells 60 units a week. Using marginal analysis, Leticia estimates the additional
revenue that will be generated by the production and sale of the 61st unit. What does
she discover? Based on this result, should she recommend increasing the level of
production?
A) $225.60; yes B) $225.60; no C) $244.00; no D) $244.00;
yes
5) A company estimates that if x thousand dollars are spent on the marketing of a 4
certain product, then Q(x) thousand units of the product will be sold, where 8
Q(x) = 4x +
1
, x2 5)
For what value of x is the sales rate minimized?
A) $9500 B) $7000 C) $15,000 D) $12,000
2
