Answer:
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
[tex]C_m(x)=\frac{dC(x)}{dx}=\frac{d}{dx}\lbrack4900+3x+0.01x^2+0.0002x^3\rbrack[/tex][tex]=\boxed{C_m(x)=3+0.02x+0.0006x^2}[/tex]
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.
[tex]C_m(100)=3+0.02(100)+0.0006(100)^2[/tex][tex]\boxed{C_m\mleft(100\mright)=11.}[/tex]
Part C:
To find the cost at x = 100, we put this value of x into C(x) and get
[tex]C(100)=4900+3(100)+0.01(100)^2+0.0002(100)^3[/tex][tex]\boxed{C\mleft(100\mright)=5500.}[/tex]
Hence, to summerise
a. 3 + 0.02 x + 0.0006 x^2
b. 11
c. 5500
