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You Answered More information is needed. x=b x=b x=a,e x=a,e Correct Answer x=b,d,f x=b,d,f There are horizontal tangent lines at x=b,d x=b,d, and f f.

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Question 6 0 / 1.66 pts The graph of a function f f is shown below. Choose the correct graph of f (x) f′ (x). IV. I. III.
You Answered V. Correct Answer II. Find where f (x)=0 f′(x)=0 (where f f has horizontal tangents); find where f (x)>0 f′(x)>0 (where f f is increasing); find where f (x)<0 f′(x)<0 (where f f is decreasing). For the function f(x) f(x) shown, there is only one location where f (x)=0 f′ (x)=0, at x=0 x=0. Therefore the graph of f (x) f′(x) must cross the x x- axis at x=0 x=0. This eliminates only answer choice V. f(x) f(x) is decreasing when x<0 x<0 and increasing when x>0 x>0, so f (x)<0 f′(x)<0 when x<0 x<0 and f (x)>0 f′(x)>0 when x>0 x>0. Only the graphs in II. and III. have this property. Notice that the graph of f(x) f(x) gets very steep near the ends. The tangent lines near the end points are nearly vertical. This makes the graph in II. a better choice than the graph in III. Question 7 1.67 / 1.67 pts The graph of f(x) f(x) is shown in the figure below. Give an estimate for f (8) f ′(8).

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−3 −3 6 6 −1 −1 Correct! 32 −32 32 32
At the point (8,3) (8,3), the tangent line is approximated by the diagonal of one grid square. The tangent line is drawn in the figure below. The slope of the tangent line is 32 −32, which is the instantaneous rate of change of f f at x=8 x=8. Question 8 0 / 1.67 pts The cost (in dollars) of extracting x x tons of ore from a copper mine is C(x) C(x). When 2000 2000 tons have been extracted, costs are increasing at the rate of \$75 \$75 per ton. Choose the mathematical expression that matches this statement. You Answered C(2000)=75 C(2000)=75 C (75)=2000 C′(75)=2000

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C (75)=−2000 C′(75)=−2000 Correct Answer C (2000)=75 C′(2000)=75 C(75)=2000 C(75)=2000 If 2000 tons are extracted, then x=2000 x=2000. The rate of increase in cost is \$75 \$75 per ton, so C (x)=75 C′(x)=75 when x=2000 x=2000. The correct expression is therefore C (2000)=75 C′(2000)=75. Notice we are not told in the problem what C(2000) C(2000) is (what the total cost is for extracting 2000 tons of ore. We are only what the rate of change is. Question 9 1.66 / 1.66 pts The function P(t) P(t) is the number of bacteria in a culture (in thousands of bacteria) t t minutes after the beginning of an experiment. Choose the statement that best interprets: P (10)=0.4 P′(10)=0.4.

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