Question

A marine manufacturer will sell N(x) power boats after spending $x thousand on advertising is given by N(x)=1000-(3780/x) for 5≤x≤30

1. Find N'(x) with appropriate units. Explain what the first derivative means in this situation. (By hand )
2. Find the number of power boats sold and the instantaneous rate of sales after spending $9,000 on advertising. Write a brief explanation of these results.
3. Use a table of values to sketch a well labelled graph of this function between $5,000 and $30,000.
4. Does the rate of power sales increase or decrease over time? Explain.

Answer 1