The relationship between the amount of money x that Cannon Precision Instruments
ID: 3196059 • Letter: T
Question
The relationship between the amount of money x that Cannon Precision Instruments spends on advertising and the company's total sales S(x) is given by the following function where x is measured in thousands of dollars.
S(x) = 0.002x3 + 0.3x2 + 4x + 500 (0 x 200)
1. Find the rate of change of the sales with respect to the amount of money spent on advertising.
S ' (x) =
2. Are Cannon's total sales increasing at a faster rate when the amount of money spent on advertising is $100,000 or $150,000?
A. $100,000
B. $150,000
Explanation / Answer
S(x) = -0.002x3 +0.3x2 +4x + 500
d[S(x)]/dx = -0.06x2 + 0.6x + 4 = Rate of change of sales wih respect to amount of money spent
Rate of change at x =100 thousands of dollars
= -0.006*10^4 + 0.6 *10^2 + 4 = -60 +60 + 4 = 4
Rate of change at x =150 thousands of dollars
= -0.006 *100*225 + 0.6*150 + 4 = -135 + 90 + 4 = -41
Sales increasing at faster rate when amount of money spent is $100,000