1.	y	=	x2(3x-1)	dy dx	=
2.	y	=	x-1(2x+1)	dy dx	=
3.	y	=	2x+1 2x-1	dy dx	=
4.	y	=	3x+2 x2-1	dy dx	=
5.	y	=	(x2-2)ex	dy dx	=
6.	y	=	x2ln x	dy dx	=
7.	y	=	ex - e-x ex	dy dx	=
8.	y	=	(2x2 - 2x)-4	dy dx	=
9.	y	=	(ln x - ex)3	dy dx	=
10.	y	=	ln (30x)	dy dx	=
11.	y	=	x+1 (2x+1)2	dy dx	=
12.	y	=	x+1 2x-1 3	dy dx	=
13.	y	=	ln(x2-x)	dy dx	=
14.	y	=	ex2-x - x	dy dx	=
15.	y	=	2x - 1 ex 2	dy dx	=

Daily sales of neon red Duffin Whallop Deluxe golfball gift-packs follows the formula

s(t)

=

20,000

-

20,000 1 + 20,000e-0.2t

,

where t is time in days since January 1, and s(t) represents the number of Duffin Whallop Deluxe gift-packs sold per day at time t.

(a) Obtain a formula for s'(t), and hence estimate how fast sales were dropping at the end of March (t = 90).

(b) How fast were sales dropping 10 days later? Approximately how many gift-packs were sold that day?

If $5,000 is invested in a mutual fund whose value is growing at a rate of 15% per year (compounded once per year), how fast is the investment growing at the end of two years? (Round your answer to the nearest cent.)

Answer: The investment is increasing at a rate of $ per year.    

The accompanying graph shows the number of transactions handled by Western Union for the years 1987-1994.^*

^* Source: Company Reports/The New York Times, September 24, 1994.

These data can be approximated by

Q(t) = 9.284e^0.117t,

where t is time in years since 1987, and Q(t) is the number of Western Union transactions (in millions) each year.

(a) According to the model, how fast was Western Union's business (as measured by annual transactions) growing in 1990? (Round your answer to the nearest 0 01 million, as in 463.23 million)
Answer: growing at a rate of million transactions each year.    

(b) What is the first year that the actual increase (from that year to the next) exceeded the rate of increase that year as predicted by the model?
Answer:    

C(x) = -0.00012x² + 30x + 50,000 dollars.

(a) What is the marginal cost at a sales level of 1000 pairs per week?

$

per pair

$

per pair

(c) At the above sales level, the marginal cost is

increasing decreasing

at a rate of $

per pair.

(d) At the above sales level, the marginal cost is

greater than Approximately equal to     less than

the average cost.

(e) In general, if the marginal cost is increasing, and there is no fixed cost, then the marginal cost is	greater than Approximately equal to     less than	the average cost.