The function P(x) = –0.015x^2 + 1.2x – 11.5 gives the profit, in thousands of dollars, when a company sells a new product at x dollars per unit. Which of the following statements best interprets the average rate of change of this function from x = 50 to x = 55? The profit increases by $375 for every $1 increase in the selling price.
The profit decreases by $375 for every $1 increase in the selling price.
The profit increases by $1875 for every $1 increase in the selling price.
The profit decreases by $1875 for every $1 increase in the selling price.

The statements that best interprets the average rate of change from x = 50 to x = 55 is (b) The profit decreases by $375 for every $1 increase in the selling price.

The profit function is given as:

Calculate P(x), when x = 50.

So, we have:

Calculate P(x), when x = 55.

So, we have:

The average rate of change from x = 50, to 55 is then calculated using:

So, we have:

Divide

The function is in 1000 units.

So, we have:

-375 implies a decrease of $375 for every $1 increase in sales

Hence, the correct statement is (b)

Read more about average rates at:

link

The profit decreases by $ 375 for every $ 1 increase in the selling price.

Step-by-step explanation:

From the definition of the secant line we get that the average rate of change of , where is the selling price of the product, measured in dollars per unit, is:

(1)

Now we evaluate the function at each bound:

x = 50

x = 55

Then, the average rate of change is:

Hence, the profit decreases by $ 375 for every $ 1 increase in the selling price.

d

step-by-step explanation:

d

step-by-step explanation:

ok so im not 100% sure but you would start by adding 5.1t and 1.9t beacuse they have the same variable. that is 7t.   then add -3.6 + 1.2 which is -2.4

so then keep that as -2.4 + 7t. i apologize if this is incorrect. best luck on your test < 3