# The total cost of manufacturing x articles is C = 47x + 300x2 - x4. Find x, for which average cost is increasing - Mathematics and Statistics

Sum

The total cost of manufacturing x articles is C = 47x + 300x2 - x4.  Find x, for which average cost is increasing

#### Solution

Given, total cost function is

C = 47x + 300x2 – x4

Average cost CA = "C"/"A"

∴ CA = (47 x + 300x^2 - x^4)/x

= (x(47 + 300x - x^3))/x

∴ CA = 47 + 300x – x3

"dC"_"A"/"dx" = 0 + 300x – 3x3

= 300x – 3x3

= 3(100 – x2)

Since average cost CA is an increasing function, "dC"_"A"/"dx" > 0

∴ 3(100 – x2) > 0

∴ 100 – x2 > 0

∴ 100 > x2

∴ x2 < 100

∴ –10 < x < 10

∴ x > – 10 and x < 10

But x > – 10 is not possible     ......[∵ x > 0]

∴ x < 10

∴ The average cost CA is increasing for x < 10.

Concept: Increasing and Decreasing Functions
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 4 Applications of Derivatives
Exercise 4.4 | Q 6.1 | Page 112