Question

The marginal cost of producing x items is given by C = x² + 4x + 4. Find the average cost and the marginal cost. What is the marginal cost when x = 7.

Answer 1

Total cost, C = x² + 4x + 4

Now, Average cost =`"C"/x`

= `(x^2+4x+4)/x`

= x + 4 + `4/x`

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

= `"d"/("d"x)(x^2 + 4x + 4)`

=`"d"/("d"x)(x^2) + 4"d"/("d"x)(x) + "d"/("d"x)(4)`

= 2x + 4(1) + 0
= 2x + 4
∴ When x = 7,
Marginal cost = `(("dC")/("d"x))_(x = 7)`

= 2(7) + 4
= 14 + 4
= 18