This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 4‘; .
MA16O Name Solon 0W5,
Rose, Spring 2011 Test #1 Please show work on all problems. lnclude units in your solutions when appropriate.
Leave answers as exact values unless you are asked to round. This test is worth 87 points. 1. (1 O pts)Consider the function f(x) shown in the graph. a. Find the average rate of change from x = 7 to x = 2. Show your calculation. AB! 1 5____)~ (—4 = L
Ax! a?  ( 7 ) ‘I
b. Find the instantaneous rate of change at x = 2. Show your calculation. 43L... 1:: = 2..
4x. om 2 2. (16) pts)Use the power rule to ﬁnd
each derivative below. Show your work, and leave your answers without
negative exponents. a. f(x)=—x3 3
42w (3)(I)’)¢
: —3 ~I ugma§= ﬁ¥
4‘
349 = 5‘ (“‘0 7L
,4!
yr:
72. d. f(x)=x9+3 W > My “72.
egm=i= 5X
x “3/1
3’65); 5 ['72) 7‘
=  é . .L . .L,
I Z 7,3/2. 3. (12 pts)The average price of a ticket to a baseball game can be approximated by
the linear function p(t) = 0.5t+ 25 where t is years after 2000 and p(t) is in dollars. a. What is p(10)? [000); a, 5’00),sz 5‘ {+256 #30
b. Interpret p(10) (explain what it means in terms of ball park tickets).
WM £30 240 YivWZd/O. c. What is the vertical intercept (the y—intercept)? 11' 9‘35" ’ d. interpret the vertical intercept? f [0) = #2 f 4‘ 25;“, w W zoo o
e. What is the slope of the line? a , 5' f. Interpret the slope. 0.5 =3 J = .413 W W » Z" w WW W 55""W 4. Acomplete graph
displays the following features with their
values intercepts turning points points of inflection
asymptotes “holes” end behavior at least one point on each
connected part of a graph (15 pts) Draw a complete graph of the function h(x) = 3(x—1)2 ~12 5 , (16 pts)Examine the graph of the function f(x) below, then circle each correct
answer. Followup each choice with an explanation. Note only the explanation earns
points. “ 5—4321 45B?891E a‘ Se'ecmne: f (3)<0 f (3)=0 f(3) does not exist
Explanation: 52(5) =l W w W b. Select one: f (x) is continuous at x = 3 f (x) is not continuous at x = 3 0. Select one: f '(3) > 0 f '(3) < 0 Explanation: a. Select one: @ f(6)=4 f(6)=0_ f(6) does not exist Explanation: w ﬂ, 5415— ,¢:U A, M w e. Select one: 1im.f(x)= 3 limf(x) =4 limf(x) = 0 )
x—>6 x—>6 x—>6 . 1—)6 ’ I PZX
I  Z4“, Pl = M
Explanation: é? M/ W M + X 19 6 ‘ / 74796‘ 74» 6*
f. Select one: f'(5) > o f'(5) < 0 f'(5) does not exist
Explanation: :1 g “ 7 f [DZ 75 :5. ‘ a— ~ MW‘LWZW 9. Select one: f ’(7) > 0 f '(7) < O f '(7) = 0 f '(7) does not exist ,
Explanation: ‘ I I ’ :/ ,7 « WW h. Select one: f (x) is not continuous atx=7
Explanation: '
ﬂy/e 94=7WW 7/ fl” 4, (18 pts) Let g(x) = —3x2
a. Find and simplify the difference quotient ___..—————g(x+ h) — g(x) 3 ON“) z ’3 (X‘H‘Y' = ‘3 (x‘+th+h3h 3(X+h)s3(x) : 5Lx"+2xh+h"! ~ 03%”)
k in
= ﬁx" '3(e17di+kzé +31?“ b. Use your result from part a and the limit definition of derivative to
determine g'(x) j(x+6)~60<>= ,4» wow—A) = +474 = 3%) 5—90 "'7," h—‘m c. Find an equation of the line that is tangent to g(x) at x = 3. Put the
equation into slopeintercept form. . (x)
inﬂate (972% Wwféw)
Its)» 22’? “’5’ 53(3)) “’(3/‘27)‘(X~<%5
[ _ ...
View
Full Document
 Spring '10
 TeresaS.McCullough
 Calculus, Derivative, pts, vertical intercept, ~I ugma§= ﬁ¥, ball park tickets

Click to edit the document details