hw 11 - silva (jrs4378) – HW11 – gualdani – (56455)...

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Unformatted text preview: silva (jrs4378) – HW11 – gualdani – (56455) This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points 3. 4 2 −4 −2 −2 If f is a function on (−4, 4) having exactly two critical points and the sign of f ′ , f ′′ are given in 4. f′ > 0 f′ < 0 f′ < 0 f′ < 0 −2 0 2 ′′ ′′ f <0 f > 0 f ′′ < 0 −4 4 2 −4 −2 −2 decide which of the following could be the graph of f . 1. 4 2 −4 −2 −2 −4 6. 2 4 −4 −2 −2 −4 4 2 −4 −2 −2 −4 002 10.0 points 2 4 5. −4 4 2 2 4 2 4 2 4 1 2. 4 2 −4 −2 −2 −4 2 4 silva (jrs4378) – HW11 – gualdani – (56455) Which of the following is the graph of x2 ? x2 − 16 6 5 4. 4 4 3 2 2 1 0 -1 −4 −2 2 4 -2 −2 -3 -4 −4 -5 -6 6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 5 5. 4 4 3 2 2 1 0 -1 −4 −2 2 4 -2 −2 -3 -4 −4 -5 -6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 5 6. 4 4 3 2 2 1 0 -1 −4 −2 2 4 -2 −2 -3 -4 −4 -5 -6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 2 f ( x) = Dashed lines indicate asymptotes. 5 1. 4 3 2 1 0 -1 -2 -3 -4 -5 -6 5 4 2 −4 −2 2 −2 −4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 4 2. 4 3 2 1 0 -1 -2 -3 -4 -5 -6 6 5 3. 4 3 2 1 0 -1 -2 -3 -4 -5 -6 4 2 −4 −2 2 −2 −4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 4 4 2 −4 −2 2 −2 −4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 003 10.0 points 4 If f is a continuous function on (−4, 4) such that (i) f has 3 critical points, (ii) f has 1 local maximum, (iii) f ′′ (x) > 0 on (−4, −2), (iv) f ′′ (x) < 0 on (0, 2), (v) (0, 1) is an inflection point, silva (jrs4378) – HW11 – gualdani – (56455) (vi) f ′ (x) < 0 on (2, 4), which one of the following could be the graph of f ? 1. 4 2 6. −4 −2 2 4 4 2 −4 −2 004 2 4 −4 −2 2 4 5. 4 2 3 2. 4 2 −4 −2 2 4 10.0 points In the following graph of a function f the xaxis and a vertical asymptote are shown, but the y -axis has been omitted. Which function f could this be? 3. 4 2 −4 −2 2 4 4. 4 2 −4 −2 2 4 1. f (x) = x 2−x √ 1 − x2 2. f (x) = − x silva (jrs4378) – HW11 – gualdani – (56455) 2−x x 1 − x2 x x 2−x 2−x x 005 10.0 points 7 6 5 1. 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 2. 4 3. f (x) = − 4. f (x) = √ graph has exactly two critical points and two inflection points, which of the following could be the graph of f ? 5. f (x) = − 6. f (x) = 6 4 2 −4 −2 −2 −4 −6 24 6 8 10 12 Which function could have -6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 12 11 6 4 2 −4 −2 −2 −4 −6 24 6 8 10 2 3π 4 3π 2π -6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 as its graph on [ 0, 2π ]? 1. f (x) = − sin x sin x 2. f (x) = cos x − 2 3. f (x) = sin x 2 + cos x sin x 2 + cos x 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3. 6 4 2 −4 −2 −2 −4 −6 24 6 8 10 4. f (x) = − 5. f (x) = -6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 6 sin x 2 − cos x 5 4. 4 6. f (x) = sin x 006 10.0 points A function f is continuous and twicedifferentiable for all x except x = −2, 2. If its 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 6 4 2 −4 −2 −2 −4 −6 24 6 8 10 12 -6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 12 11 silva (jrs4378) – HW11 – gualdani – (56455) 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 5. 5 6 4 2 −4 −2 −2 −4 −6 2 46 8 10 12 2. -6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 12 11 007 10.0 points 3. Which of the following rational functions has a vertical asymptote x = 5 and a slant asymptote y = 2x? 1. f (x) = 2. g (x) = 3. k (x) = 2x2 − 10x + 1 x−5 2 x2 − x (x − 5)2 2 x3 −x x−5 4. 4. none of these 5. j (x) = 6. h(x) = 2x + 1 x+5 2 x2 x−5 008 10.0 points 5. Which of the following is the graph of f ( x) = 1 −x x when dashed lines indicate asymptotes? 1. 6. silva (jrs4378) – HW11 – gualdani – (56455) 011 10.0 points 6 7. A rectangular dog pound with three kennels as shown in the figure 8. consists of a rectangular fenced area divided by two partitions. Determine the maximum possible area of this pound if 64 yards of chain link fencing is available for its construction. 009 10.0 points 1. max area = 124 sq.yards 2. max area = 125 sq.yards 3. max area = 128 sq.yards 4. max area = 127 sq.yards 5. max area = 126 sq.yards 012 10.0 points A Pine Car Derby car rolls along a track with velocity v ( t) = 3 + 2 t − t 2 feet per second. If it starts at time t = 0, after how many seconds will its position be maximized? 1. t = 3 seconds 2. t = 0 seconds 3. none of these 4. t = 1 second 5. t = 2 seconds 6. t = 9 seconds A 6′′ × 6′′ square sheet of metal is made into an open box by cutting out a square at each corner and then folding up the four sides. Determine the maximum volume, Vmax , of the box. 1. Vmax = 21 cu. ins. 2. Vmax = 16 cu. ins. 010 10.0 points 3. Vmax = 36 cu. ins. 4. Vmax = 31 cu. ins. Find the positive number such that the sum of 5 times this number and 8 times its reciprocal is as small as possible. silva (jrs4378) – HW11 – gualdani – (56455) 5. Vmax = 26 cu. ins. 013 10.0 points 4. max. area = 18 sq. inches √ 5. max. area = 18 3 sq. inches 6. max. area = 36 sq. inches 015 10.0 points 7 The canvas wind shelter The rectangle in the figure is to be constructed for use on Padre Island beaches. It is to have a back, two square sides, and a top. If 96 square feet of canvas are available, find the depth of the shelter for which the space inside is maximized assuming all the canvas is used. 1. depth = 9 feet 2 (x, y ) 2. depth = 2 feet 3. depth = 8 feet 4. none of these 5. depth = 4 feet 014 10.0 points is formed with adjacent sides on the coordinate axes and one corner on the graph of 30x + 16 x2 + 1 Find the maximum possible area of this rectangle. y= 61 sq. units. 2 65 2. max area = sq. units. 2 1. max area = 3. max area = 31 sq. units. 4. max area = 63 sq. units. 2 A rectangle is inscribed in an equilateral triangle so that one side of the rectangle lies on the base of the triangle. Find the maximum area the rectangle can have when the triangle has side length 12 inches. √ 1. max. area = 9 3 sq. inches 2. max. area = 9 sq. inches √ 3. max. area = 36 3 sq. inches 5. max area = 32 sq. units. 016 10.0 points A company manufacturing lawn-mowers find that its weekly cost and demand equations are x C (x) = 20 + 24x, p(x) = 60 − 5 silva (jrs4378) – HW11 – gualdani – (56455) when it sells x lawn-mowers per week. If the company can sell all the lawn-mowers it manufactures, determine the maximum profit from the sale of these lawn-mowers. 1. maximum profit = $1605 2. maximum profit = $1590 3. maximum profit = $1595 4. maximum profit = $1585 5. maximum profit = $1600 017 10.0 points 8 A trailer rental agency rents 12 trailers per day at a rate of $36 per day. It discovers that for each $6 increase in rate, one fewer trailer is rented. Determine the maximum income the rental agency can obtain. 1. maximum income = $486 2. maximum income = $510 3. maximum income = $492 4. maximum income = $498 5. maximum income = $504 6. none of these ...
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