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maximized or whether total profits must be positive or negative. Quiz Score: 20 out of 25 Previous Next Submission Details: Score for this attempt: 17.5 out of 25 Submitted Sep 30 at 2:38pm This attempt took 42 minutes. Question 1 0 / 2 pts Choose the function f f that has a point of inflection on the interval (a,b) (a,b) and such that f (x)>0 f′(x)>0 on the interval (a,b) (a,b).
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IV. You Answered II. V. III. Correct Answer I. The function must be increasing and have a point of inflection on the interval (a,b) (a,b). Only I. and II. have a point of inflection on the interval (a,b) (a,b). II. is
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decreasing, and I. is increasing. The correct answer is I. Note that in IV. f ′′ (x)=0 f″ (x)=0 because this choice is linear. Question 2 2 / 2 pts At which values of x x is the function f(x) f(x) discontinuous? f(x)= x 2 −3x+2x 2 −1 f(x)=x2−3x+2x2−1 x=−1,1,2 x=−1,1,2 x=−1 x=−1 f(x) f(x) is continuous for all x x . x=0 x=0 Correct! x=−1,1 x=−1,1 The function f(x) f(x) is discontinuous where the denominator is equal to zero: f(x)= x 2 −3x+2x 2 −1 = (x−2)(x−1)(x−1)(x+1) f(x)=x2−3x+2x2−1=(x−2)(x−1)(x−1) (x+1)
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The denominator equals zero at x=−1,1 x=−1,1. Note that we cannot cancel the (x−1) (x−1) terms (although we could if we were calculating the limit as x→1 x→1 because when we take the limit, we don't care what happens when x=1 x=1, only as x x approaches 1. Question 3 2 / 2 pts Let C(q) C(q) represent the cost and R(q) R(q) represent the revenue, in dollars, of producing q q items. Suppose C(100)=4000 C(100)=4000 and R(100)=5500 R(100)=5500. If C (100)=20 C′(100)=20 and R (100)=24 R′(100)=24, approximately how much profit is earned by producing 101 101 items? $1604 Correct! $1504 $404 $5600
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$5505 Producing 100 100 items yields a profit of 5500−4000=1500 5500−4000=1500. Marginal profit at q=100 q=100 is R (100)−C (100)=24−20=4 R′(100)−C ′(100)=24−20=4 dollars per unit. Adding one unit of production when 100 units are being produced (and sold) adds approximately $4 $4 in profit. Producing and selling 101 101 units yields a profit of approximately $1504 $1504. Question 4 2 / 2 pts Calculate the limit: lim x→2 3ln(x−1) limx→23ln(x−1) −1 −1 1 1 Correct! 0 0 3 3
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The limit does not exist. The limit does not exist. lim x→2 3ln(x−1)=3ln(1)=3⋅0=0 limx→23ln(x−1)=3ln(1)=3 0=0 Question 5 2 / 2 pts Evaluate the limit: lim h→0(h+2) 3 −8h limh→0(h+2)3−8h The limit does not exist. The limit does not exist. 1 1 8 8 Correct! 12 12 0 0 lim h→0 (h+2) 3 −8h=lim h→0 h 3 +6h 2 +12h+8−8h=lim h→0 h 3 +6h 2 +12hh =lim h→0 h(h 2 +6h+12)h=lim h→0 h 2 +6h+12=0+0+12=12 limh→0(h+2)3 −8h=limh→0h3+6h2+12h+8−8h=limh→0h3+6h2+12hh=limh→0h(h2+6h+12)h=limh→0 h2+6h+12=0+0+12=12 Question 6 2 / 2 pts
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A function g g has g(8)=22 g(8)=22, g (8)=6 g′(8)=6, and g ′′ (x)<0 g″(x)<0 for all x x. Which of the following is a possible value for g(10) g(10)? (Assume the function is continuous and the first and second derivatives exist for all x x.) 36 Correct!
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