If the cost function for producing a product is $C ( x ) = x ^ { 3 } - \frac { 1 } { 2 x ^ { 2 } } + 3 x + 2$ find the answer closest to the marginal cost at a production level of 10 units.
A) -697
B) 30
C) 293
D) 297
E) 697

Question

Quizplus · Accepted Answer

The marginal cost is the derivative of the cost function. The derivative of $C(x) = x^3 - \frac{1}{2x^2} + 3x + 2$ is $C'(x) = 3x^2 + \frac{1}{x^3} + 3$. Evaluating this at $x = 10$, we get $C'(10) = 3(10)^2 + \frac{1}{10^3} + 3 = 300 + 0.001 + 3 = 303.001$, which is closest to 297.

If the Cost Function for Producing a Product Is C(x)=x3−12x2+3x+2C ( x ) = x ^ { 3 } - \frac { 1 } { 2 x ^ { 2 } } + 3 x + 2C(x)=x3−2x21​+3x+2

If the Cost Function for Producing a Product Is $C ( x ) = x ^ { 3 } - \frac { 1 } { 2 x ^ { 2 } } + 3 x + 2$