A horticulturist conducted an experiment to determine the effects of different amounts of fertilizer on the yield of a plot of green onions.He modeled his results with the function $Y(x)=-0.5(x-2)^{2}+5$
where Y is the yield in bushels and x is the amount of fertilizer in pounds.What are $Y(0.75)$
and $Y^{\prime}(0.75)$
? Give your answers to two decimal places, specify units.
A)4.22 bushels, 1.25 bushels/pound, respectively
B)4.22 bushels, 6.25 bushels/pound, respectively
C)1.25 bushels, 1.56 bushels/pound, respectively
D)1.25 bushels, 4.22 bushels/pound, respectively

Question

A horticulturist conducted an experiment to determine the effects of different amounts of fertilizer on the yield of a plot of green onions.He modeled his results with the function $Y(x)=-0.5(x-2)^{2}+5$
 where Y is the yield in bushels and x is the amount of fertilizer in pounds.What are $Y(0.75)$
 and $Y^{\prime}(0.75)$
 ? Give your answers to two decimal places, specify units.
A)4.22 bushels, 1.25 bushels/pound, respectively
B)4.22 bushels, 6.25 bushels/pound, respectively
C)1.25 bushels, 1.56 bushels/pound, respectively
D)1.25 bushels, 4.22 bushels/pound, respectively

Quizplus · Accepted Answer

To find $Y(0.75)$, substitute $x = 0.75$ into the given function: $Y(0.75) = -0.5(0.75-2)^2 + 5 = -0.5(-1.25)^2 + 5 = -0.5(1.5625) + 5 = -0.78125 + 5 = 4.21875$, which rounds to 4.22 bushels. To find $Y'(x)$, differentiate the given function: $Y'(x) = -0.5 \cdot 2(x-2) = -(x-2)$. Then, $Y'(0.75) = -(0.75-2) = 1.25$ bushels/pound.

A Horticulturist Conducted an Experiment to Determine the Effects of Different