# If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4. - Mathematics and Statistics

Sum

If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4.

#### Solution

Total cost function C = 5x3 + 2x2 + 1

Average cost = "C"/x

=(5x^3 + 2x^2 + 1)/x

= 5x2 + 2x +1/x

When x = 4, Average cost = 5(4)2 + 2(4) + 1/4

= 80 + 8 + 1/4

= (320+32+1)/4

= 353/4

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

= "d"/"d"x (5x^3 + 2x^2 + 1)

=5"d"/"d"(x^3) + 2"d"/"d"(x^2) + "d"/"d"(1)

=5(3x2) + 2(2x) + 0
= 15x2 + 4x

When x = 4, marginal cost = (("dC")/("d"x))_("x" = 4)

= 15(4)2 + 4(4)
= 240 + 16
= 256
∴ The average cost and marginal cost at x = 4 are 353/4 and 256 respectively.

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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 9 Differentiation
Miscellaneous Exercise 9 | Q III. (8) | Page 124