# The cost of producing x articles is given by C = x2 + 15x + 81. Find the average cost and marginal cost functions. Find marginal cost when x = 10. Find x for which the - Mathematics and Statistics

Sum

The cost of producing x articles is given by C = x2 + 15x + 81. Find the average cost and marginal cost functions. Find marginal cost when x = 10. Find x for which the marginal cost equals the average cost.

#### Solution

Given, cost C = x2 + 15x + 81

Average cost = "C"/x=(x^2+15x+81)/x

= x + 15 + 81/x

and Marginal cost = ("dC")/("d"x)

= "d"/("d"x)(x^2 + 15x + 81)

= "d"/("d"x)(x^2) + 15d/("d"x)(x) + "d"/("d"x)(81)

= 2x + 15(1) + 0
= 2x + 15
When x = 10,

Marginal cost = (("dC")/("d"x))_(x = 10)

= 2(10) + 15
= 35
If marginal cost = average cost, then

2x + 15 = x + 15 + 81/x

∴ x = 81/x

∴ x2 = 81
∴ x = 9   …[∵ x > 0]

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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 9 Differentiation
Exercise 9.2 | Q II. (11) | Page 123
Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 9 Differentiation
Miscellaneous Exercise 9 | Q III. (10) | Page 124