Ünite 7: Applications of Derivative — Önemli Kavramlar

The derivative of the total cost function, C'(x), which represents the approximate cost of producing one additional unit of a product. For example, if C(x) = x^2/8 + 3x + 98, the marginal cost is C'(x) = x/4 + 3.

The derivative of the total revenue function, R'(x), which represents the additional revenue generated by selling one extra unit of a product. It is calculated from the revenue function R(x) = p(x) * x.

The derivative of the total profit function, P'(x), representing the additional gain obtained by producing and selling one more unit. It is equal to marginal revenue minus marginal cost: P'(x) = R'(x) - C'(x).

A dimensionless measure of the responsiveness of quantity demanded to a change in price, calculated as Ep = |(dq/dp) * (p/q)|. For example, for q(p) = 320 - 4p at p = 50, the elasticity is 1.66, meaning a 1% price increase reduces demand by 1.66%.

A state where the price elasticity of demand is less than 1 (Ep < 1), meaning consumers are insensitive to price changes. In this region, a percentage increase in price results in a smaller percentage decrease in demand, causing total revenue to rise.

A state where the price elasticity of demand is greater than 1 (Ep > 1), indicating that consumers are highly sensitive to price changes. In this region, a percentage increase in price leads to a larger percentage decrease in demand, causing total revenue to fall.

A state where the price elasticity of demand is exactly equal to 1 (Ep = 1). At this point, a percentage change in price results in an identical percentage change in demand, and total revenue is unaffected by small price changes.

An extreme economic state where the price elasticity of demand is infinite (Ep = infinity). The demand curve is horizontal, meaning any increase in price above the market rate causes demand to drop immediately to zero.

An extreme economic state where the price elasticity of demand is zero (Ep = 0). The demand curve is vertical, meaning the quantity demanded remains completely unchanged regardless of the price level.

The production and sales level where a company's total revenue equals its total cost (R(x) = C(x)), resulting in zero net profit or loss. It is found by solving the equation R(x) - C(x) = 0 for x.

The market condition where the quantity demanded by consumers equals the quantity supplied by producers. It is represented graphically by the intersection of the supply and demand curves.