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# Summary - Applications of Differentiation

Demand is the relationship between the quantity demanded and the price of a commodity.

SUMMARY

Demand is the relationship between the quantity demanded and the price of a commodity.

Supply is the relationship between the quantity supplied and the price of a commodity.

Cost is the amount spent on the production of a commodity.

Revenue is the amount realised by selling the output produced on commodity.

Profit is the excess of total revenue over the cost of production.

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

Equilibrium price is the price at which the demand of a commodity is equal to its supply.

Marginal cost is interpreted as the approximate change in production cost of ( x + 1)th unit, when the production level is x units.

Marginal Revenue is interpreted as the approximate change in revenue made on by selling of ( x + 1)th unit, when the sale level is x units.

A function f(x) is said to be increasing function in the interval [a, b] if x1 < x2 Ō¤╣ f (x1 ) =< f (x2) for all x1, x2 Ō▓ł  [a,b]

A function f(x) is said to be strictly increasing in [a, b] if x1 < x2 Ō¤╣ f (x1 ) < f (x2) for all x1, x2 Ō▓ł  [a,b]

A function f(x) is said to be decreasing function in [a,b] if x1 < x2 Ō¤╣ f (x1 ) >= f (x2) for all x1, x2 Ō▓ł  [a,b]

A function f(x) is said to be strictly decreasing function in [a, bif x1 < x2 Ō¤╣ f (x1 ) > f (x2) for all x1, x2 Ō▓ł  [a,b]

Let f be a differentiable function on an open interval (a,b) containing c and suppose that f'ŌĆÖ(c) exists.

(i) If f '(c) = 0 and f "(c) > 0, then f has a local minimum at c.

(ii) If f '(c) = 0 and f "(c) < 0,then f has a local maximum at c.

A function f(x,y) of two independent variables x and y is said to be homogeneous in x and y of degree n if for t > 0  f (tx , ty ) = t n f ( x, y)

If u = f ( x , y) is a homogeneous function of degree n, then The partial elasticity of demand  q with respect to p1 is defined to be The partial elasticity of demand q with respect to p2 is defined to be   Tags : Applications of Differentiation , 11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation
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11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation : Summary - Applications of Differentiation | Applications of Differentiation