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The crop yield, Y, (in bushels) for various amounts, x (in pounds per 100 square feet) of fertilizer used in 18 different plots of land is as shown in the table below. The graph of the data can be modeled by
Y(x)=-0.017x^2+1.0765x + 3.8939
What is the optimal amount of fertilizer to apply for maximum crop yield?
The max crop yield occurs when x=-b/2a = -[1.0765]/[-2*0.017] = 31 lbs per 100
Explain or show how you decided.