The total revenue in Rupees received from the sale of x units of a product is given by R(x)=13 x

step 1 The question says the total cost CX in rupees associated with the production of X units of an it

The total revenue in Rupees received from the sale of x...

Key Concepts

Revenue Function

A revenue function is a mathematical representation of the total income earned from selling a product, where the input variable typically denotes the number of units sold and the output gives the total revenue. This function enables businesses to analyze how revenue varies with sales volume and is foundational in both economic theory and operational decision-making.

Marginal Revenue

Marginal revenue refers to the additional revenue gained from selling one extra unit of a product. It is calculated as the derivative of the revenue function with respect to the quantity sold, providing a measure of the revenue change for an incremental increase in output. This concept is critical for optimizing production levels and pricing strategies in economics.

Differentiation

Differentiation is a core concept in calculus involving the process of finding a derivative, which quantifies the rate at which a function changes with respect to changes in its input. In the context of economic functions like the revenue function, differentiation helps in determining marginal effects, such as marginal revenue.

Power Rule for Differentiation

The power rule is a basic technique in differentiation used to find the derivative of polynomial functions. It states that for a term of the form ax^n, the derivative is n*ax^(n-1). This rule simplifies the process of evaluating the marginal impact of changes in sales on total revenue by efficiently computing the derivative of each term in the revenue function.

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