# Therefore f1149 f1149 question 7 0 2 pts the

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Therefore f(11)=49 f(11)=49. Question 7 0 / 2 pts The following figure shows the graph of y=f(x) y=f(x). At one of the labeled points, dydx dydx is negative and d 2 ydx 2 d2ydx2 is positive. Which point is it?

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V. You Answered II. I. III. Correct Answer IV.
Recall the Leibniz notation: dydx =f (x) dydx=f′(x) and d 2 ydx 2 =f ′′ (x) d2ydx2=f″(x). We want a point where dydx <0 dydx<0 ( f f is decreasing) and d 2 ydx 2 >0 d2ydx2>0 ( f f is concave up). IV. is the only choice. Question 8 2 / 2 pts The following figure shows the graph of y=f(x) y=f(x). Give the signs of the first and second derivatives. Each derivative is either positive everywhere, negative everywhere or zero everywhere. f (x) f′(x) is positive; f ′′ (x) f″(x) is zero. f (x) f′(x) is zero; f ′′ (x) f″(x) is positive. f (x) f′(x) is positive; f ′′ (x) f″(x) is negative. Correct!

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f (x) f′(x) is positive; f ′′ (x) f″(x) is positive. f (x) f′(x) is negative; f ′′ (x) f″(x) is positive. f(x) f(x) is increasing and concave up everywhere, so f (x)>0 f′(x)>0 and f ′′ (x)>0 f″(x)>0. Question 9 0 / 2 pts The table below shows y y as a function of x x, so that y=f(x) y=f(x). According to the data in the table, is the derivative of f(x) f(x) negative or positive? Is the second derivative negative, positive, or zero? x 0 5 10 15 20 25 30 35 y = f(x) 40 38 32 23 12 -1 -18 -45 You Answered The first derivative is positive; the second derivative is negative. The first derivative is negative; the second derivative is positive. The first derivative is negative; the second derivative is zero. The first derivative is positive; the second derivative is positive. Correct Answer
The first derivative is negative; the second derivative is negative. f(x) f(x) is decreasing, so f (x)<0 f′(x)<0. Notice that the size of the decrease is getting larger as x x gets larger, so f (x) f′(x) is getting more negative and f (x) f′(x) is decreasing. This means that f ′′ (x)<0 f″(x)<0 and f(x) f(x) is concave down. This may be more clear by looking at a plot plot of the points in the table Question 10 2 / 2 pts Let P(t) P(t) be the cost of a gallon of gasoline, where t t is the year. Choose the best interpretation of the statement: For t≥2013 t≥2013, P (t)<0 P′ (t)<0 and P ′′ (t)>0 P″(t)>0. Note: This example is not necessarily based on real-world prices. Use only the information given in the problem.

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Since 2013, the price of gas has been rising, but the rate that the price has been increasing has been slowing. Since 2013, the price of gas has been increasing at a faster and faster rate. In 2013, the price of gas was falling. Since then, the price of gas has been increasing. Since 2013, the price of gas has been declining at a faster and faster rate. Correct! Since 2013, the price of gas has been falling, but the rate that the price has been falling has been slowing.

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