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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.)

Respuesta :

theoooooo
=> 
|∆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.

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