Test Bank Text Appendix C – Differential Calculus
TEXT APPENDIX C – Differential Calculus Techniques in Management
MULTIPLE CHOICE
1. Differentiate the following TC function: TC = 150 + 200 Q – 4 Q2 + .6 Q3
a. dTC/dQ = 200 – 8Q + 1.8 Q2
b. dTC/dQ =-8 + 1.8 Q2
c. dTC/dQ = 200
d. dTC/dQ = 200 – 4Q + .6Q2
e. dTC/dQ = 1.8 Q2
2. The total revenue function (where Q = output), is: TR = 400 Q – 4 Q2
a. TR is maximized at Q = 20
b. TR is maximized at Q = 30
c. TR is maximized at Q = 40
d. TR is maximized at Q = 50
e. TR is maximized at Q = 60
3. The following is a cubic demand function in P. Find the derivative dQ/dP of: Q= 4+3P-.5P2 + .02P3.
a. dQ/dP = 4 + 3P – P + .06P2
b. dQ/dP = 3
c. dQ/dP = 3 – P + .06P2
d. dQ/dP = .06P2
e. dQ/dP = .06
4. If the first derivative of Y with respect to X is: dY/dX = –4·X2, then the second derivative is:
a. -4
b. –8•X
c. –4•X
d. –8·X2
e. -8
5. The second derivative of the function (d2Y/dX2 ) is negative at the optimal solution of X=22. Therefore,
we know that the solution X=22, where the first derivative equals zero…
a. must be a minimum.
b. must be a maximum.
c. may be either a maximum or a minimum.
d. would be nothing, because the second derivative is negative.
Test Bank Text Appendix C – Differential Calculus
6. Differentiate the following function with respect to Q: TC = 50 + 100Q -6Q2 +.5Q3
a. dTC/dQ = 50 + 100 -6Q + .5Q2
b. dTC/dQ = 100 –12Q + 1.5Q2
c. dTC/dQ = 50 + 100 -2Q + 3Q2
d. dTC/dQ = 100