Question

Help solve A & B) a) find marginal cost functionB) find the marginal cost at x= 100

Answer 1

Step-by-step explanation:

Part A;

The marginal cost function is the derivative of the cost function.

The x derivative of the cost function C_m( x) is

`C_m(x)=(dC(x))/(dx)=(d)/(dx)\lbrack4900+3x+0.01x^2+0.0002x^3\rbrack`
`=\boxed{C_m(x)=3+0.02x+0.0006x^2}`

Part B:

To find the marginal cost at x = 100, we put this value of x into the marginal cost function we found in part A.

`C_m(100)=3+0.02(100)+0.0006(100)^2`
`\boxed{C_m\mleft(100\mright)=11.}`

Part C:

To find the cost at x = 100, we put this value of x into C(x) and get

`C(100)=4900+3(100)+0.01(100)^2+0.0002(100)^3`
`\boxed{C\mleft(100\mright)=5500.}`

Hence, to summerise

a. 3 + 0.02 x + 0.0006 x^2

b. 11

c. 5500