Ch 4B discussion problems 1. Your muscle car gas mileage (in miles per gallon) is given as M(x) of speed x mph, where M(x) = 3000 x + 3600 x 1 Calculate M'(x) and M'(10), M'(60) and M'(70). What do the answers tell you about the car? Hint: use quotient rule or modify M(x) and use chain rule to find M'(x). 2. Marginal Revenue The weekly revenue from the sale of rubies at Royal Ruby Retailers (RRR) is increasing at a rate of $40 per $1 increase in price and the price is decreasing at a rate of $0.75 per additional ruby sold. What is the marginal revenue? Be sure to state units of measurements and interpret the result. See example below: Suppose a company's weekly is given as a function of price p, and p is given as a price of quantity x items, i.e. R(p(x)). If revenue is increasing by $20 per $1 increase in price and price is decreasing by $5 per each additional item sold, find marginal revenue. Solution: dR dR dp (this is according to chain rule in section 4.3 as derivative of \"outside\" function = dx dp dx (or change of revenue with respect to price)* derivative of \"inside\" (or change of price with respect to number of items x)) dR = $20 per $1 increase in price = $20/$1 = 20 dp dp = $5 per additional item sold = -$5 per item = -5 (it's negative since price is decreasing) dx dR = 20(5) = 100 = -$100 per item dx Revenue is decreasing by $100 per each additional item sold (marginal revenue R' = -100)