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

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

A function *f*(*x*) is said to be increasing function in
the interval [*a*, *b*] if *x*_{1}* *<* x*_{2}* **âŸ¹** f (x*_{1}* *)* =*<* f*
(*x*_{2})* *for all* x*_{1},* x*_{2}* **â²ˆ *[a,b]

A
function *f*(*x*) is said to be strictly increasing in [*a,* *b*] if *x*1* *<* x*2* **âŸ¹** f (x*1* *)* *<* f* (*x*2)* *for all* x*1,* x*2* **â²ˆ *[a,b]

A
function *f*(*x*) is said to be decreasing function in [*a,b*] if *x*1* *<* x*2* **âŸ¹** f (x*1* *)* >=** f* (*x*2)* *for all* x*1,* x*2* **â²ˆ *[a,b]

A
function *f*(*x*) is said to be strictly decreasing function in [*a*, *b*] *x*1* *<* x*2* **âŸ¹** f (x*1* *)* >** f* (*x*2)* *for all* x*1,* x*2* **â²ˆ *[a,b]

Let *f* be a differentiable function on an
open interval (*a,b*) containing *c* and suppose that *f*'â€™(*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 *p*_{1} is defined to be

The
partial elasticity of demand *q* with
respect to *p*_{2} 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

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