menu
bartleby
search
close search
Hit Return to see all results

The sales of a product S(in thousands of dollars) are given byS= 600x/x+40where x is the advertising expenditure(in thousands of dollars)(a) Find the rate of change of sales with respect to advertising expenditure.(b) Use the second derivative to find how this rate is changing at x=20.(c) Interpret your result in part (b).

Question

The sales of a product S(in thousands of dollars) are given by

S= 600x/x+40

where x is the advertising expenditure(in thousands of dollars)

(a) Find the rate of change of sales with respect to advertising expenditure.

(b) Use the second derivative to find how this rate is changing at x=20.

(c) Interpret your result in part (b).

check_circleAnswer
Step 1

Given:

The function that repesents the sales of a product S is 

 

600x
S =
x +40
help_outline

Image Transcriptionclose

600x S = x +40

fullscreen
Step 2

a)

Obtain the derivative of the given function with respect to x.

600x
dx{x+ 40
(x+ 40)(600)-(600x) (1)
(x+40)
24000
(x+40)
Thus, the rate of change of sales with respect to the advertising expenditure is
24000
(x+40)
help_outline

Image Transcriptionclose

600x dx{x+ 40 (x+ 40)(600)-(600x) (1) (x+40) 24000 (x+40) Thus, the rate of change of sales with respect to the advertising expenditure is 24000 (x+40)

fullscreen
Step 3

b)

Derivate the above obtained S’ w...

d
S"
dx(x+40)
24000
(x40) (0)(24000) (2 (x + 40))
(x40)
-48000
(x+40)
help_outline

Image Transcriptionclose

d S" dx(x+40) 24000 (x40) (0)(24000) (2 (x + 40)) (x40) -48000 (x+40)

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Calculus

Other

Sorry about that. What wasn’t helpful?