MATH151 Fall 2022 Common Exam III Version A FIRST NAME print UIN LAST NAME print INSTRUCTOR SECTION NUMBER DIRECTIONS No calculators cell phones smart watches headphones or other electronic devices may be used and must be put away TURN OFF cell phones and put them away If a cell phone is seen during the exam your exam will be collected and you will receive a zero In Part I mark the correct choice on your ScanTron using a No 2 pencil The scantrons will not be returned therefore for your own records also record your choices on your exam In Part II present your solutions in the space provided Show all your work neatly and concisely and clearly indicate your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it Be sure to fill in your name UIN section number and version letter of the exam on the ScanTron form THE AGGIE HONOR CODE An Aggie does not lie cheat or steal or tolerate those who do Signature 1 Part I Multiple Choice 4 points each 1 Suppose f x has a domain of all real numbers and f x x3 x 2 5 x2 6x 16 Find the x coordinates of the inflection points of f a x 8 only b x 0 only c x 8 and x 0 d x 8 x 0 and x 2 e x 0 and x 2 e3x 3x cos x 2 Find limx 0 2x3 x2 a 5 b 0 c d 27 e 2 3 Find the value s of c that satisfy the conclusion of the Mean Value Theorem for the f x x3 x on the interval 0 3 733 a b 2 c 1 d 103 e 3 2 x x 1 on x 3 on 1 4 4 Find the absolute maximum and minimum values of f x 6 0 25 a Absolute maximum is 10 absolute minimum is 1 b Absolute maximum is 10 absolute minimum is 6 c Absolute maximum is 9 absolute minimum is 0 d Absolute maximum is 6 absolute minimum is 1 e Absolute maximum is 10 absolute minimum is 0 5 Set up the limit to find the area under the graph of f x a lim 3 3 3 i b lim 3 1 3 i c lim 4 4 4 i d lim 3 4 3 i e lim 4 3 4 i n i 1 n i 1 n i 1 n i 1 n n n n n n n n n n n n n n n n i 1 3 The graph below is the derivative f x of a continuous function f whose domain is all real numbers Use this graph to answer questions 6 and 7 6 Find the value s of x where f has a local maximum a x a and x p b x c and x s c x b and x r d x d e 7 Find the interval s where f is concave up a b d r b a c p s c b d r d c q e c p Cannot be determined 4 g x dx 5 find 5 f x 3g x dx 1 2 5 5 2 1 1 f x dx 1 f x dx 4 and 8 Given a 20 b 10 c 10 d 19 e 11 9 Find the interval s where g x ex x2 x 5 is decreasing a 3 2 b 3 0 0 2 c 3 0 d 3 2 e 3 5 2x 3 x4 x x Find f 0 if f 1 2 10 Suppose f x 13 a 42 b 38 c 35 d 4 e 0 11 Estimate the area under the graph of f x 25 x2 from x 2 to x 4 using 3 rectangles of equal width and midpoints a 132 b 134 c 128 d 110 e 192 12 Which of the following is true a Every function attains an absolute minimum and absolute maximum on a closed interval b A left Riemann sum is always an underestimate d G x arccos x is the only antiderivative of g x 1 c Any limit of the form evaluates to 0 1 x2 e If f 3 0 and f 3 4 then f has a local minimum at x 3 6 x x 5 x tan 13 Find lim a 5 b 0 c 1 d 1 e 5 14 Use the graph of f below to evaluate f x dx 6 3 a 7 b 11 c 16 d 19 e 10 7 15 An object is traveling at 10 m s when it starts to accelerate at 6 m s 2 How far does the object travel before reaching a speed of 40 m s a 125 m b 50 m c 150 m d 110m e 200 m 16 Find the critical numbers of f x x2 5 x 6 2 a x 1 6 b x 0 6 c x 6 12 d x 0 1 6 e x 0 6 12 8 Part II Work Out Problems Directions Present your solutions in the space provided Show all your work neatly and concisely and box your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 17 6 points Find the most general antiderivative of f x sec x tan x 5 3x 6 sin x 1 x2 x 18 9 points Find lim x 0 cos x 3 x 2 9 for which f x x 5 x 3 3 x 1 19 10 points Consider the function f x x and f x 2x 18 3 2 x 3 4 a What is the domain of f domain b Determine the interval s on which f is increasing or decreasing If there are none write DNE increasing decreasing c Determine the x coordinates of any local extrema If there are none write DNE local maximum at x local minimum at x d Determine the interval s on which f is concave upward or concave downward If there are none write DNE concave down concave up e Determine the x coordinates of any inflection points If there are none write DNE inflection point at x 10 20 11 points The top and bottom margins of a poster are each 2 in and the side margins are 1 in The poster is to have a total area of 128 in2 Find the dimensions of the poster that will maximize the printed area Justify that your answer gives a maximum Do not write in this table Question Points Awarded Points 1 16 64 6 17 18 9 10 19 20 11 100 Total 11
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