Calculus question

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 + 0.7x² + 5x + 500      (0 ≤ x ≤ 200)

Find S '(x), the rate of change of the sales with respect to the amount of money spent on advertising.

S '(x) =  

$$45

 

 

At what rate (in dollars per thousand dollars of advertising) are Cannon's total sales increasing when the amount of money spent on advertising is $90,000?

$   per thousand dollars of advertising

At what rate (in dollars per thousand dollars of advertising) are Cannon's total sales increasing when the amount of money spent on advertising is $140,000?

$   per thousand dollars of advertising

Answer 1

S(x)=-.002x^3+.7x^2+5x+500

S'(x)=-.006x^2+1.4x+5

For every $1000 dollars , x=1

For $90000 x=90

For $140000 x=140

S'(90)=-.006(90)^2+1.4(90)+5

S'(140)=-.006(140)^2+1.4(140)+5