# APPENDIX C – Differential Calculus Techniques in Management

Business

Q 1Q 1

Differentiate the following TC function: TC = 150 + 200 Q - 4 Q

^{2}+ .6 Q^{3}A)dTC/dQ = 200 - 8Q + 1.8 Q^{2}B)dTC/dQ =-8 + 1.8 Q^{2}C)dTC/dQ = 200 D)dTC/dQ = 200 - 4Q + .6Q^{2}E)dTC/dQ = 1.8 Q^{2}Free

Multiple Choice

A

Q 2Q 2

The total revenue function (where Q = output),is: TR = 400 Q - 4 Q

^{2}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 = 60Free

Multiple Choice

D

Q 3Q 3

The following is a cubic demand function in P.Find the derivative dQ/dP of: Q= 4+3P-.5P

^{2}+ .02P^{3}. A)dQ/dP = 4 + 3P - P + .06P^{2}B)dQ/dP = 3 C)dQ/dP = 3 - P + .06P^{2}D)dQ/dP = .06P^{2}E)dQ/dP = .06Free

Multiple Choice

C

Q 4Q 4

If the first derivative of Y with respect to X is: dY/dX = -4·X

^{2},then the second derivative is: A)-4 B)-8•X C)-4•X D)-8·X^{2}E)-8Free

Multiple Choice

Q 5Q 5

The second derivative of the function (d

^{2}Y/dX^{2})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.Free

Multiple Choice

Q 6Q 6

Differentiate the following function with respect to Q: TC = 50 + 100Q -6Q

^{2}+.5Q^{3}A)dTC/dQ = 50 + 100 -6Q + .5Q^{2}B)dTC/dQ = 100 -12Q + 1.5Q^{2}C)dTC/dQ = 50 + 100 -2Q + 3Q^{2}D)dTC/dQ = 100Free

Multiple Choice