Question

1. For the following functions, find ∆y (the exact change) and dy (the approximate change from a linear approximation) for the given functions.

(i) f(x) = x + 4/x , x = 2, ∆x = .1

(ii) f(x) = x/ln (x² + 3), x = 3, ∆x = .5

2. A pretzel vendor at a dodgers game sells 920 pretzels per game at a price of $4.00. For every $0.50 decrease in price an additional 20 pretzels are sold. The cost for producing x pretzel is C(x) = 350 − 52x + .01x²

(i) Write the demand function. That is, express the price as a function of the number of pretzels sold.

(ii) To make the maximum profit, how many pretzels should the vendor sell at each game?

(iii) To make the maximum profit, what price should the pretzels be set at?

Answer 1