Suppose P(x) represents the profit on the sale of x Blu-ray discs. If P(1,000) = 5,000 and P'(1,000) = −3, what do these values
tell you about the profit? P(1,000) represents the profit on the sale of Blu-ray discs. P(1,000) = 5,000, so the profit on the sale of Blu-ray discs is $ . P'(x) represents the as a function of x. P'(1,000) = −3, so the profit is decreasing at the rate of $ per additional Blu-ray disc sold.
We are told that P(x) is the profit of saling x blu ray discs. P(1000) is our profit for selling 1000 blu ray discs. So, our profit is 5000. Recall that the derivative P'(x) represents the rate at which the function P(x) is increasing/decreasing (increasing if P'(x) is positive, or decreasing otherwise) by increasing the values of x. In this case P'(1000)=-3, so the profit will decrease -3 if we increase x in one unit.
If Shelly wants 6 rose bushes, and each bush costs $40, then you can multiply 6 by 40 to find the total amount of money Shelly will spend on them if she plants them herself. 6 x 40 = 240. You can then subtract 240 from 600 to find the amount of money she saves. 600 - 240 = 360
