2 A horticulturist conducted an experiment to determine the

2.

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. Compute and interpret Y(0.75) and Y\'(0.75)? Give your answers to two decimal places, specify units.

Solution

As

Y(x) = -0.5(x-2)^2 + 5, then
Y\'(x) = 2 - x

Thus,

Y(0.75) = 3.875
Y\'(0.75) = 2 - 0.75 = 1.25

Thus, this means that we project that if we 0.75 lbs of fertilizer, we expect about 4 (from 3.875) bushels.

For Y\'(0.75), this means that, if we add a few more fertilizer, say x lbs of fertilizer, we expect that there will be an increase of 1.25x bushels in the yield.