Government economists in a certain country have determined that the demand equation for soybeans is given by p = f (x) = 57 2x2 + 1 where the unit price p is expressed in dollars per bushel and x, the quantity demanded per year, is measured in billions of bushels. the economists are forecasting a harvest of 2.4 billion bushels for the year, with a possible error of 10% in their forecast. use differentials to approximate the corresponding error in the predicted price per bushel of soybeans. (round your answer to one decimal place.)

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Business

Boozer

26 February, 12:45

Government economists in a certain country have determined that the demand equation for soybeans is given by p = f (x) = 57 2x2 + 1 where the unit price p is expressed in dollars per bushel and x, the quantity demanded per year, is measured in billions of bushels. the economists are forecasting a harvest of 2.4 billion bushels for the year, with a possible error of 10% in their forecast. use differentials to approximate the corresponding error in the predicted price per bushel of soybeans. (round your answer to one decimal place.)

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Belinda Cummings · Answer 1

=>

|∆p| = |dp/dx|∙|∆x|

= | d{ 56 / (2∙x² + 1) ]/dx | ∙ |∆x|

= | 56∙ (-1) ∙2∙ (2x) / (2∙x² + 1) ² ] | ∙ |∆x|

= | - 224∙x / (2∙x² + 1) ² | ∙ |∆x|

for

x = 1.9

∆x = 0.1∙1.9 = 0.19

|∆p| = 224∙1.9 / (2∙ (1.9) ² + 1) ² | ∙ |0.19| = 1.197

That is about twice of your result. Maybe you forget a factor 2 in the numerator while taking the derivative.