Question

The marginal cost of producing the xth box of floppy discs is 20+x+ 1/x²

What is the general form of the cost function? (Use K for the constant of integration.)
c(x)=

Answer 1

The general form of the cost function can be obtained by integrating the given marginal cost function: c(x) = 20x + 1/2x² - 1/x + K, where K is the constant of integration.

Step-by-step explanation:

The general form of the cost function can be obtained by integrating the given marginal cost function.

The marginal cost function is given as: m(x) = 20 + x + 1/x²

To find the cost function, we need to integrate the marginal cost function.

Integrating each term separately, we get:

1. Integrating 20 with respect to x gives 20x.
2. Integrating x with respect to x gives 1/2x².
3. Integrating 1/x² with respect to x gives -1/x.

The general form of the cost function, c(x), is the sum of the three integrals:

c(x) = 20x + 1/2x² - 1/x + K, where K is the constant of integration.