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Lesson-4: Business Applications of Differentiation
Lesson Objectives:
After studying this lesson, you should be able to:
 State the key concepts related to business applications of
differentiation;
 Apply the techniques of differentiation to solve business
problems.

Key Concepts
Total costs (TC): Total cost is the combination of fixed cost and variable
cost of output. If the production increases, only total variable cost will
increase in direct proportion but the fixed cost will remain unchanged
within a relevant range.
Total revenue (TR): Total revenue is the product of price/demand
function and output.
Profit: Profits are defined as the excess of total revenue over total costs.
Symbolically it can be expressed as, P (profit) = TR – TC. i.e., (Total
Revenue – Total Cost)
The rules for finding a maximum point tell us that P is maximized when
the derivative of the profit function is equal to zero and the second
derivative is negative. If we denote the derivatives of the revenue and
cost functions by dTR and dTC we have,
‘P’ is at a maximum when dTR – dTC = 0. This equation may be written
as dTR = dTC.
The derivative of the total revenue function must be equal to the
derivative of the total cost function for profits to be maximized.

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