This** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
**Unformatted text preview: **Name MATH 151 Second Hourly--Spring 2013 Instructor: Dr. A. Silverstein 3/13/13
Instructions: Show all work on the test paper. Put your name on the test paper and all scratch sheets. Decimal answers are permitted unless stated otherwise; show the values accurate to 4 places.
The total points possible on this test are @. GOOD LUCK” ~ 1. For
f(:c) = (2:1: + 4)(5:1: — 3)
ﬁnd the derivative both ways and show the answers are equivalent:
a) Byalgebra ﬂag )2 to x V , Q X, 4— 20 x ’12, a /0>< €o F’Kx22aox;+/I-/ ”"’+l‘lx»éz, b) By Product Rule M’w‘vic = 1(0’96‘3) r 572wa
7* lé’ﬂ’évf—Zﬂx P 2’0 (10) 2. Find an equation of the tangent line to the curve :1 {,‘L O ,4, 4. l «,6-
= 0.2553 — 5:132 + 2 -
at m : — 1. Simplify your answer.
~ 2..
:: mf zf/zyé-j: ‘6’.)4 -1034, @ﬂW}
My (10)
c7 914:)(‘14‘ é: é/ .2 ,2,[‘./) 3., {Xvi/2342,
:4 $2
9944 [a4 .,, 7- a, 2, ef-fL
pnf-o
M27. 1 ,3,‘7_,r-«—3,L my”: -3,L,¢0,éj (42w
r3Lz—4m6+e
$40.6 +/0,é 7.44 ab yzzaéx+2¥ 4. For f (as) = 1:2 — 316 + 5, ﬁnd f’ (2) using the deﬁnition of the derivative. Show all detail. Use the
Power Rule as a check only. You may break up the steps as follows:
21) Find f (2 + h) and simplify your answer. 7&(L—PLV): (L‘fA)L’3(Z/‘7LA)+(
ch+Lt)(z+L7) ”(a 9A #f
T. ¢+y2+ae~¢ ~3Z+j (4)
'—' 12.14% + 3
b) Find f(2). (1)
7552/): «191-3 (v) +5 = ‘9‘—éf§ ; 3
M
c) Find the difference quotient and simplify.
%(L¢A/»—F(z) 3 Qchk +2) / 3
A A
AHA, , {$ch = LN <3)
“7:“ ' Z ,9. d) Use the difference quotient to ﬁnd f’ (2). £9»; (it/+1) : 0 +1 =- / (3)
lid 5) Mg; {xz‘w3x+5) = Lx~3 aux: 9,: zcw~3= l/
5. A snow removal company earns an annual proﬁt (in thousands of dollars) of
13(33) : 0.251:2 — 33: + 100
where ac represents the number of customers in hundreds.
a) Find the yearly proﬁt if there are 400 customers. waef
(96%): O‘RC‘I)”‘Z~ 3C¢}+/OO W 39/ m
b) Find the marginal pro 1t at the 400 customer level. W?J:/f’(a€)t‘ﬁlx:3 [WW
Wadﬁ’f: , (4)»3 z/e/B zl‘f’ (6) \\ 9/. 7, <3> w/ﬁ/ﬂm) 5 “/‘9‘00 c) Interpret your answer to (b) Give full units. Mat/7 151--Second H0ur/y—s’13—page 3 8. The demand for theater tickets depends on the price. The following equation shows the number of
tickets a: in (hundreds) that can be sold if the price per ticket is p dollars:
3669): x = 100 — 0.005102
a) Find the rate of change in the demand at price level $110. “db/M4 Wotazw 15/<P)=~~.oor(2ir) (6) OJP=HO: ~.905{2L0)2 ~/./ 7(/
b) Explain why this value is negative in terms of the relation of price and demand.
\ N WM tin/v WW%/ (3) (105) ﬁ‘OI’f wwwwwqﬂp gamma/0M [/0WW W 54, Wt
fa.) bkL fZZH/W at am M M
#0;me W Zzéew Math 151——Second Hour/y—s’JJ—page 5 ...

View
Full Document

- Fall '13
- Capozzi
- Math