cost function C = – Find x , when the total cost is minimum. . Let u log . Using Euler’s theorem show that x u y u ∂ ∂ + ∂ ∂ = .
. Verify ∂ ∂∂ = ∂ ∂∂ u x y u y x for u x y . I f f x y xy x y ( , ) = , then show that f yy ( , ) Summary z Demand is the relationship between the quantity demanded and the price of a commodity. z Supply is the relationship between the quantity supplied and the price of a commodity.
z Cost is the a mount spent on the production of a commodity. z Revenue is the amount realised by selling the output produced on commodity. z Profit is the excess of total revenue over the cost of production. z Elasticity of a function y = f ( x ) at a point x is the limiting case of ratio of the relative change in y to the relative change in x z Equilibrium price is the price at which the demand of a commodity is equal to its supply.
z Marginal cost is interpreted as the approximate change in production cost of th h unit, when the production level is x units. - - Applications of Differentiation z Marginal Revenue is interpreted as the approximate change in revenue made on by selling of x th h unit, when the sale level is x units. z A function f ( x ) is said to be increasing function in the interval [ a , b ] if f x f x & h for all x x a b e @ z A function f ( x ) is said to be strictly increasing in [ a , b ] if f x f x & h for all x x a b e @ z A function f ( x ) is said to be decreasing function in [