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.

Answer 1

Answer:

The marginal cost when x=8 is:

                          375

Step-by-step 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,

$\dfrac{d}{dx} x^n=nx^{n-1}$  )

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

Hence, we get:

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