# The first derivative is positive the second

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The first derivative is positive; the second derivative is negative. You Answered The first derivative is negative; the second derivative is negative. Correct Answer

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The first derivative is negative; the second derivative is positive. The first derivative is positive; the second derivative is positive. f(x) f(x) is decreasing, so f (x)<0 f′(x)<0. Notice that the size of the decrease is getting smaller as x x gets larger. That is f (x) f′(x) is getting less negative. This means the rate of change f (x) f′(x) is increasing, so f(x) f(x) is concave up and f ′′ (x)>0 f″(x)>0. This may be more clear by looking at a plot plot of the points in the table Question 10 2 / 2 pts
Let S(t) S(t) be the total capacity of installed solar power in the US (in TeraWatts), where t t is the year. Choose the best interpretation of the statement: For t≥2009 t≥2009, S (t)>0 S′(t)>0 and S ′′ (t)>0 S″(t)>0. Note: This example is not necessarily based on real data. Use only the information given in the problem. Correct! Since 2009, the installed capacity of solar power has been increasing at a faster and faster rate. Since 2009, the installed capacity of solar power has been increasing at a steady rate. Since 2009, the installed capacity of solar power has been decreasing at a faster and faster rate. Since 2009, the installed capacity of solar power has been increasing, but the rate of increase has been declining. Since 2009, the installed capacity of solar power has been decreasing, but the rate of decrease has been declining. S (t)>0 S′(t)>0 means the installed capacity has been increasing. S ′′ (t)>0 S″ (t)>0 means that the rate of increase has also been increasing, so installed capacity has been increasing at a faster and faster rate. Question 11 1.5 / 1.5 pts

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Let N=f(t) N=f(t) be the total sales of a product in thousands, where t t is the number of months since the product was launched. Eight months after the product is launched, total sales have reached 410,000 410,000 and sales per month are lower than in previous months, and continue to decline after 8 8 months. Choose the best expression to match this statement. f (8)<410 f′(8)<410 and f ′′ (8)=0 f″(8)=0 . f (8)>0 f′(8)>0 and f ′′ (8)>0 f″(8)>0 . f (410)>8 f′(410)>8 and f ′′ (410)<8 f″(410)<8 . f (8)<0 f′(8)<0 and f ′′ (8)<0 f″(8)<0 . Correct! f (8)>0 f′(8)>0 and f ′′ (8)<0 f″(8)<0 . At t=8 t=8, total sales are increasing (sales per month are not zero), so f (8)>0 f′(8)>0. Since sales per month are declining, f ′′ (8)<0 f″(8)<0 and f(t) f(t) is concave down at t=8 t=8. Question 12 1 / 1 pts
If for a function f(t) f(t), the second derivative is negative ( f ′′ (t)<0 f″(t)<0), then the derivative, f (t) f′(t) is decreasing. Correct! True False True: The sign of f ′′ (t) f″(t) tells us whether f (t) f′(t) is increasing or decreasing, because f ′′ (t) f″(t) is the derivative of f (t) f′(t). So if f ′′ (t)<0 f″(t)<0, then f (t) f′(t) is decreasing, and the function f(t) f(t) is concave down.

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