ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Chapter-1 of Section-C. Step by step Solutions of ML Aggarwal ISC Class 12 Mathematics for Exercise Questions with Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

## ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Chapter-1 of Section-C

Board | ISC |

Class | 12 |

Subject | Mathematics |

Ch-1 Sec-C | Applications of Calculus |

Session | 2024-25 |

Topics | Solutions of ML Aggarwal |

### Applications of Calculus in Commerce and Economics

**INTRODUCTION: ** Differential calculus is used while determining the rate of change of a given function (dependent variable) due to change in one of the independent variables. Integration is the inverse of differentiation and it involves finding a function whose rate of change is given. In this chapter, we shall start with the a few basic concepts of economics—fixed and variable cost, average cost, revenue, profit etc., and then go on to marginal functions (marginal cost and marginal revenue) using first derivative. We shall use second derivatives to find minimum costs and maximum revenue or maximum profit.

**Demand function:**

Various economic studies show that the quantity demanded of a commodity depends upon many factors, viz., price of the commodity, consumer’s income, taste of the consumer, price of other related commodities etc. To simplify things, we will consider the relationship between demand and price of the commodity only, assuming that all other factors remain constant.

**Revenue function:**

Revenue means the amount received by a company by selling a certain number of units of a commodity. Let p be the price per unit and x be the number of units sold. Then total revenue

R or R(x) = p . x If price p is constant, then R(x) is obviously a straight line. If price p varies with demand x, then p = f (x) so that R or R (x) = (demand) . (price) = x f (x)

** BREAKEVEN ANALYSIS:**

Usually, as the companies incur capital costs (fixed costs), they are in loss when the production/sale is low. However, as the production/sale increases, the average cost comes down, and beyond a certain point, the company starts making profit. This leads us to breakeven point analysis. The breakeven point is the level of production where the revenue from sales is equal to the total cost of production. At this point, the company makes neither profits nor losses.

### Exercise – 1.1

ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Chapter-1 of Section-C

### Exercise – 1.2

ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Chapter-1 of Section-C

### Exercise – 1.3

### Exercise – 1.4

### Chapter Test

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