Question

Suppose that the total proft in hundreds of dollars from seling x isems is given by P(x)=3x 2 −4x+6 Complete parts a through d below a. Find the avecage rate of change of profit as x changes from 4 to 6 per item b. Find the average rate of change of protit as x changes trom 4 to 5 per item c. Find and interpeet the instantaneous rate of change of profit with respect to the number of tems produced when x=4 (This number is called the margiral profit at x=4 ) per item What does this result mean? Choose the correct answer below.

A. When 4 items are sold, the prohit is decreasing at the rate of 5 per item
B. When items are sold for $, the protit is decreasing at the rate of $4 per item
C. When 4 items are sold, the profit is increasing at the rate of 4 per item
D. When items are sold for 5 the profit is increasing at the rate of $4 per ifem: d. Find the marginal profit at x=6 per item

Answer 1

To find the average rate of change of profit, calculate the difference in profit at x=6 and x=4, then divide by the difference in x values.

Step-by-step explanation:

To find the average rate of change of profit as x changes from 4 to 6 per item, we need to find the difference in profit at x=6 and x=4 and divide it by the difference in x values.

Step 1: Calculate the profit at x=4 and x=6 using the given profit function P(x)=3x^2-4x+6.

Step 2: Subtract the profit at x=4 from the profit at x=6 to find the difference in profit.

Step 3: Divide the difference in profit by the difference in x values (6-4=2) to find the average rate of change of profit.