Question

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

Answer 1

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.