# Solve the following example: If the total cost function is given by; C = 5x3 + 2x2 + 7; find the average cost and the marginal cost when x = 4. - Mathematics and Statistics

Sum

Solve the following example: If the total cost function is given by; C = 5x3 + 2x2 + 7; find the average cost and the marginal cost when x = 4.

#### Solution

Total cost function, C = 5x3 + 2x2 + 7

Average cost = "C"/x

=(5x^3 + 2x^2 + 7)/x

= 5x2 + 2x + 7/x

When x = 4,

Average cost = 5(4)2 + 2(4) + 7/4

= 80 + 8 + 7/4

= (320 + 32+ 7)/4

= 359/4

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

="d"/("d"x)(5x^3 + 2x^2 + 7)

= 5"d"/("d"x) (x^3) + 2"d"/("d"x)(x^2) + "d"/("d"x)(7)

= 5(3x2) + 2(2x) + 0
= 15x2 + 4x
When x = 4, Marginal cost = (("dC")/"dx")_ (x = 4)
= 15(4)2 + 4(4)
= 240 + 16
= 256
∴ the average cost and marginal cost at x = 4 are 359/4 and 256 respectively.

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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. (4) | Page 122