Each of Exercises 61 through 68 involves either the chain rule for partial derivatives or the incremental approximation formula for functions of two variables.

The demand for a certain product is Q(x, y) = 200 − 10x² + 20xy units per month, where x is the price of the product and y is the price of a competing product. It is estimated that t months from now, the price of the product will be x(t) = 10 + 0.5t dollars per unit while the price of the competing product will be y(t) = 12.8 + 0.2t² dollars per unit.

a. At what rate will the demand for the product be changing with respect to time 4 months from now?

b. At what percentage rate

will the demand for the product be changing with respect to time 4 months from now?

Transcribed Image Text:

(1),0001 Q(t)