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Test1_solutions

# Test1_solutions - 4‘ MA16O Name Solon 0W5 Rose Spring...

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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. Follow-up each choice with an explanation. Note only the explanation earns points. “ -5—4-3-2-1 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 ‘ / 74-796‘ 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 slope-intercept form. . (x) inﬂate (972% Wwféw) Its)» 22’? “’5’ 53(3)) “’(3/‘27)‘(X~<%5 [ _ ...
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Test1_solutions - 4‘ MA16O Name Solon 0W5 Rose Spring...

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