Question

p ot an iten Hu between the price shows the relationship a demand curve on 3.5) In economics, the number x (in thousands) of such items that can be sold at that price. Suppose that the demand a commodity is given by the formula x2000-p3,valid for p S 12. Note that the radical in this equation is a cube root, not a square root.) (a) Use implicit differentiation to find the rate of change of p with respect to x (that is, an expression for dp d or p(x). Note that you will probubly 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 (x12). 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).

Answer 1

2000-p3 ) differentiate with respect to x. 0(2000-) 1(2000-33-1 d -(2000- 3 -(2000-p3)T ргар 1 dp -p-a (2000-p3) dz (b) x-10 to x 12 change în χ1S 2. change in price dp 10-(2000-PY when xo-10 p 10 ap-2x10" (2000-103)? price 1s decrease