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Question: The cost price, selling price of x C(x S(x dollars respectively where C(x x 2 + 9x and S(x x 2 + 10x x What is the marginal profit on selling 2 units of the item? Steps to derive 1 Cost function is C(x x 2 + 9x 2 Selling function is S(x x 2 + 10x 3 Profit function is P(x x x x 2 + x 4 The marginal profit on selling x x 0 = 2 units of the item is lim h → 0 P ( x 0 + h ) - P ( x 0 ) h 5 = lim h → 0 P ( 2 + h ) - P ( 2 ) h 6 = lim h → 0 [ ( 2 + h ) 2 + ( 2 + h ) + 1 ] - 7 h 7 = lim h → 0 h 2 + 5 h h 8 = lim h → 0 h 9 = 0 + 5 = 510 So, the marginal profit on selling 2 units is $5.
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