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(Step-by-Step) Effect of Advertising on Sales. The relationship between the amount of money x that Cannon Precision Instruments spends on advertising and

Question: Effect of Advertising on Sales. 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 function

\[S(x)=-0.002 x^{3}+0.6 x^{2}+x+500 \quad(0 \leq x \leq 200)\]

where \(x\) is measured in thousands of dollars. Find the rate of change of the sales with respect to the amount of money spent on advertising. Are Cannon's total sales increasing at a faster rate when the amount of money spent on advertising is (a) $100,000 or (b) $150,000?

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