Find the marginal cost, marginal revenue, and marginal profit functions. C(x) = 7x; R(x) = 9x − 0.001x2

Given:

The cost function is

The revenue function is

To find:

The marginal cost, marginal revenue, and marginal profit functions.

Solution:

We know that,

The marginal cost, marginal revenue, and marginal profit functions are the derivatives of cost, revenue and profit functions respectively.

Marginal cost function is

Marginal revenue function is

Marginal profit function is

Therefore, the marginal cost, marginal revenue, and marginal profit functions are , and respectively.