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I / i MUH 122 Test 1 ver. A

Winter 05

: Name K E Y ' - f l .McAr ID#/

i You must show all work in a neat and organized manner using proper notation to receive full ' credit. No books or notes are allowed.

1. The table lists the approximate number of people employed in the United States durin,o the period 1995-2001, on July 1 of each year (t = 5 represents 1995):

Compute and interpret the average rate of change of P(t) over the period 1995-2000. Be sure to state units of measurement. (7 pts.)

'2 fiP,&-pffa9 : G c i C- &A',' 003 N*.AMJ! l ~ j r ~ r ~ . i + m y t . ~ ~ ~ - J ; + I

7, The following curve is a model of the total prison population in time in years (t = 0 represents 1980). (6 pts.)

Year, t Employment,P(t)

(millions)

a) Circle the correct answer. Over the period [16,20], the instantaneous rate of change of N is

6 120

5 117

./------------ (A) increasing ' (B) decreasing "x,

L -------,..-- - b) Circle the correct answer. Over the period [O,28], the instantaneous rate of change of N is

*-<,.- - --, . .-----s---- --.--.-- -.--- --. ,&A) increasin~ s d then decreasd -_ --- (B) decreasing and then increasing (C) a1 ways increasing (D) always decreasing

7 123

c) According to the model, the total state prison population was increasing fastest around what year?

I

8 125

9 130

10 132

11 132

MIX 122 Test 1 ver. A Winter 05

3. Use the definition of the derivative to find fl(x) if f(x) = 2$ + 5. You must show work to receive credlt. (8 pts,)

4. Use the graph to answer the following. (10 pts.)

a) lim f(x) = - 1 . 8 . ' - I i : : : j i , . . . ! . . . . ..,

b) lim f(x) = ? ;-L+ 3 i, . , 'Ti ?>: LF$i,

- 3 ,-I - u

c) lim f(x) = ;; +- 7;T-i p b!;

' G .-.-- . - .T .-

d) Aia f(x) = - A 7.

h42X 122 Test 1 ver. A

5. Find the derivative of each fimction. Do not sim~lifv vour answers. (6 pts. each)

MTH 122 Tegt 1 ver. A Winter 05

6. A car wash f i calculates that its daily profit (in d o l l ~ ) m the number of workers it employs according to the formula P = -1 00n + 25n2 - b.O&Id a) Find the marginal product hct ion. (3 pts;] .

b) Cdcdate the m a r p l product at an employment level of 40 workers and interpret the . '4 red&. (4 ma

7. Paramount Electronics has an annual profit given by P = -1 00,000 + 50Wq - 0.25q2

where q is the of laptop computers it sells each yew. The rider of laptop computers it can make and sell each year depends on the number m of electrical engineers Paramount employs, according to the quation

q = XD+ 0.01n2 r) Use tbe chaja ~ , I B * hfind

c b w 8 (4 pQ.1

b) S b l d P m Mectronics hire additional electrical en-eeers? Just$@ pour answer. (3 pts.)

MTK 122 Test 1 ver. 4 Winter 05

8. The graph of the derivative functh~, ?(x), is given. Deternine the x coordinates of all , '

stationary and singular points off and class* each as a relative maximum, relative m i n a , or neither. (Assume that f(x) is de fd&exa t in ere in [-3,3].) (6 pts)

9. The graph of the second deriv~tivejimcti~ro, fll(x), is @ven. Detericndne the x coordinates of dl points of inflection of f (x), if my. ( A s m e that f@) is clefifled and continuous everywhere in [-3,3].) (6 pts)

10. Hercules Films is decidmg on the price of the video release of its film Bride of the Son of Frankenstein. Marketing estimates that at a price of p dollars it can sell q = 200,001t10,OOOp copies, but each copy costs $4 to make. What price will give the greatest profit? What is the . maximurn profit. You must pve an appropriate equation and verie that your answer gives a maximum value to receive full credit. (9 pis.)

MTH 122 Test 1 ver, A Winter 05

11. a) Label all relative md absolute extrerna and points of inflection b) Use calculus to find the coordinates of these points exactly. - You must h w your work far dZJg cidit. (1Opts.S

dx) - 2x3 + 3x2 - 1 2 ~ - 10, domain [-4,3)