Question

The total cost to produce x handcrafted wagons is C(x) = 110 + 7x - x^2 + 2x^3. Find the marginal cost when x = 8.

1016
1126
485
375

Answer 1

The marginal cost when x=8 is:

375

Explanation:

We know that the marginal function for a cost function C(x) at x=a

is given by:

C'(x) at x=a

Here we have the cost function C(x) as:

`C(x)=110+7x-x^2+2x^3`

Now we find the derivative of C(x) with respect to x.

i.e.

`C'(x)=0+7-2x+6x^2`

( Since,

`(d)/(dx) x^n=nx^(n-1)` )

`C'(x)=7-2x+6x^2`

Hence, we get:

`C'(8)=7-2* 8+6* (8)^2\\\\i.e.\\\\C'(8)=7-16+384\\\\C'(8)=375`