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by: Vivien Bradtke V


Vivien Bradtke V
Texas A&M
GPA 3.6


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This 10 page Study Guide was uploaded by Vivien Bradtke V on Wednesday October 21, 2015. The Study Guide belongs to MATH 142 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 58 views. For similar materials see /class/226052/math-142-texas-a-m-university in Mathematics (M) at Texas A&M University.

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Date Created: 10/21/15
Li Chen S39pring 2006 Week In Review 7 Test 2 Review Covers sections 21 24 31 35 41 43 O This review gives one or two examples from each section It is NOT a thorough review by itself but rather some additional practice problems that you can study along with your homework and lecture notes O The problems in Weekln Review 5 and 6 are also good review problems for the exam Review Problems 1 Consider the function f x x 2 Round the answers to three decimal places a Find the average rate of change of f between x 2 and x 4 b Estimate f 3by using a small interval c Find f 3by using derivative formulas d Find the equation of the line tangent to x at x 3 Li Chen S39pring 2006 2 The graph off is given below at which value of x is a x greatest b x least c f x greatest d f x least e f x greatest t f x least 3 a If the graph below is of x which of the following has the largest value fquot2 f 3 K3 f 3 f 0 b If the above graph is of x where is x increasing c If the above graph is of x where is x concave up 1 If the above graph is of f x where is x increasing e If the above graph is of f x where does fx have in ection points f If the above graph is of f x where does x have local maxima g If the above graph is of f x where is x concave up Li Chen S39pring 2006 4 Letfx 3x3 5x2 x9 a Find all critical points of x and state what type of critical points they are local max local min or either b Find the in ection points c Find the intervals at which x is decreasing and concave up at same time d Find the globe maximum and globe minimum of x on the interval 2 l 5 The value of A Toyota minivan purchased in 2005 can be approximated by the function Vt 25085 where t is the time in years from the date of purchase and Vis the value in thousands of dollars a Evaluate and interpret V4 b Evaluate and interpret V 394 Li Chen S39pring 2006 6 The table below shows the world gold production G ft as a function of year t tyear 1987 1990 1993 1996I 1999 Gmilliontroyounces 53 70 73 74 81 a Does f I appear to be positive or negative What does this mean in terms of gold production b In which time interval does f I appear to be greatest c Estimate f 1999 Give units and interpret the answer in terms of gold production d Use the estimate value of f 1999 to estimate ZOOO and 2005 and interpret the answers 7 The following figure shows the tangent line approximation to x near x a a Find afa and f 39a b Estimate Z l and fl 98 Are these under or overestimates Which estimate would you eXpect to be more accurate and why y 3x7 2 Li Chen S39pring 2006 8 Sketch a possible graph of a function that satisfies all of the given conditions f60f01f3940 f xgt0 for 0ltxlt4 f xlt0 for xlt0 andxgt4 fquotxgt0 for 2ltxlt2 fquotxlt0 for xlt 2 andxgt2 fx gt3asx gt oo 9 The following graph is of x Sketch the graph of f x f x Li Chen S39pring 2006 10 Find the value of a so that the function fx xeax has a critical point at x 3 11 If f and g are functions whose graphs shown on the right find a MD if hx gfx b h2 if hx f x2 0 W1 if hx 3 f xgx dh 3 39fh M 1 x x Li Chen S39pring 2006 12 During a u outbreak in a school of 763 children the number of infected children I was expressed in terms of the number of susceptible but still healthy children S by the expression 2 l921n S 763 What is the maximum possible number of infected children Find the derivatives for the following functions 13 fx2i3x 5ex 39 x 14 gx ln2x 3 cos x 1n 3 5 y 1539 2Vlnxxex 1 Li Chen S39pring 2006 16 252 39g 3 2 17 Hln I3 18 gx 2 3xz2 sin3x2 x24x 19 Find f x for f x e Li Chen S39pring 2006 Answers 1 a 28 b 246367 c 246355 d y 246355x 499 2 a x1 b x5 0 x2 d 963 9 961 0 x5 3 a f 393 is the largest value bfx is increasing on 00 2 and 2 oo cfx is concave up on 0 oo df393 is the largest value efx is increasing on 3 0 ffx has in ection points at x i2 gfx has a local maximum at x 0 hfx is concave up on 3 0 4 afx has two critical points x 19 and x 1 f19 is a local maximumf1 is a local minimum b The in ection point is at x 59 cfx is decreasing and concave up on 59 1 d The globe maximum is 90535 and the globe minimum is 37 5a V4 1305 which means the car will be worth about 13050 in 2009 b V4 2 121 which means the value ofthe car will be decreasing at a rate of 2121 per year in 2009 Or in year 2010 the car will be worth about 11040 6 a f 39t appears to be positive because according to the table gold production is increasing b The derivative the rate of change appears to be greatest between 1987 and 1990 cf391999 m 2333 million troy ouncesyear In 1999 gold production was increasing at a rate of approximately 2333 million troy ounces per year df2000 m 83333 million troy ounces f2005 m 94998 million troy ounces 7 a 2 1 and 3 bf2 1 07 underf198 106 over and is better 8 9 Graph 10 a 13 11 a 12 b 4 c 2 d 13 12 306 children 13 f39x 7 22 5xz3 7e l4 g xl3sinx x 15 y 7lnx xeX 1 ml eX xex x 7 z32157zz512 7 zz6z13 7 232 7 232 2z5 7 1 zz512 E 16 HQ 17 H 39z 18 y 712x2 7 3x2 sin3x2 6x2 7 3x2 2 cos3x2 19 fquotx 25 2x2 8x 9 Li Chen S39pring 2006 If you nd any mistakes please let me know Th anksl lich en2jle0tamu edu


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