The relationship between the amount of money x that Cannon Precision Instruments spends on advertising and the company's total s
ales S(x) is given by the following function where x is measured in thousands of dollars. S(x) = −0.002x3 + 0.4x2 + 9x + 500 (0 ≤ x ≤ 200) Find the rate of change of the sales with respect to the amount of money spent on advertising.
The rate of change of the sales S(x) with respect to the amount of money spent on advertising x is then the derivative of S(x) with respect to x. What we have to calculate is S'(x).
We know that the derivative of is (where a is a constant), and the derivative of a sum is the sum of the derivatives, so we can calculate the derivative of each term independently:
