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Question: Government economists in a certain country have determined that the demand equation for soybeans is given by $p = f(x) = \frac{55}{2x^2 + 1}$ 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. Determine the corresponding error in the predicted price per bushel of soybeans. (Round your answer to one decimal place.)

This is my second question on similar problems and I am still having problems fully understanding this concept. So how would I go about step by step on answering this question. After seeing how wrong I was on my last question, I'd like to just start fresh and see how this is answered. Thanks for all the help in advance.

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Hoping that I am not wrong, you are asked to evaluate the change of $$f(x) = \frac{55}{2x^2 + 1}$$ if $x$ changes by $10$% around $x=2.4$ that is to say if $\Delta x=0.24$. Using derivatives, you have $$\frac {df(x)}{dx}=-\frac{220 x}{\left(2 x^2+1\right)^2}$$ and then $$\Delta f(x)=-\frac{220 x}{\left(2 x^2+1\right)^2}\Delta x$$ So, if $x=2.4$,$f(2.4)=4.39297$,$\frac {df(x)}{dx}=-3.36841$.

I am sure that you can take from here.

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  • $\begingroup$ Thanks a lot for the help! $\endgroup$ – Kenshin Jul 11 '14 at 8:17
  • $\begingroup$ You are very welcome ! $\endgroup$ – Claude Leibovici Jul 11 '14 at 8:56

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