Question

Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) = 5x² - 7x + 5. Complete parts a through d below.

a. Find the average rate of change of profit.

Answer 1

The average rate of change of profit can be found by calculating the difference in profit between two values of x divided by the difference in x.

Step-by-step explanation:

The average rate of change of profit can be determined by finding the slope of the profit function. In this case, the profit function is P(x) = 5x² - 7x + 5. To find the average rate of change, we need to find the difference in profit between two values of x divided by the difference in x.

Let's say we want to find the average rate of change between x = a and x = b. The formula is:

Average rate of change = (P(b) - P(a))/(b - a)

Substituting the values into the formula:

Average rate of change = (5b² - 7b + 5 - 5a² + 7a - 5)/(b - a)

This is the formula to find the average rate of change of profit for any two values of x.