derivative word problem?

Question

A company's revenue from car sales, C (in thousands of dollars), is a function of advetising expenditure, a, in thousands of dollars, so C=ƒ(a).

(a) What does the statement ƒ'(100)=2 mean in practical terms? How about ƒ'(100)=0.5?

(b) Suppose the company plans to spend about $100,000 on advertising. If ƒ'(100)=2, should the company spend more or less than $100,000 on advertising? What if ƒ'(100)=0.5?

Help, especially with (b)! Thank you!

Answer 1

(a) The statement ƒ'(100)=2 mean that at the advetising expenditure level of 100 thousand dollars, the revenue increase from car sales would be 2 dollars for every dollar of increased advetising expenditure.
The statement ƒ'(100)=0.5 mean that at the advetising expenditure level of 100 thousand dollars, the revenue increase from car sales would be 0.5 dollar for every dollar of increased advetising expenditure.

(b) Suppose the company plans to spend about $100,000 on advertising. If ƒ'(100)=2, the company should spend more than $100,000 on advertising, because the return is higher (obviously from reasoning in (a)). On the other hand, if ƒ'(100)=0.5, the company should spend less than $100,000 on advertising.