2. (Based on 3.5) In economics, a demand curve shows the relationship between the price p of an item and the number.r (in thousands) of such items that can be sold at that price. Suppose that the demand curve for a commodity is given by the formula x = tl 2000-23, valid for p 12. (a) Use implicit differentiation to find the rate of change of p with respect to r (that is, an expression for (Note th_the radical in this equation is a cube root, not a square root.) dpor (x). Note that you will probably have to use the chain rule. (b) Use differentials and the result of part (a) to estimate the amount by which the price should be changed if the seller wishes to increase the number of items sold from 10,000 ( x = 10 ) to 12,000 (x-12). Round the price to the nearest penny, and clearly indicate whether the change in price would be an increase or a decrease (describe in words, not just as a plus or minus sign).
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