Interpreting the question

[Sophie]

Hello

I am once again having problems interpreting the question, my continuing battle unfortunatly. Also I have a hard time placing rate of change with marginal revenue at the right point in the questions. Anyway here is the question and my attempt at it.


Suppose that a company that spends $x on advertising sells $s os merchandise where s(x) = (-3x^3) + (270x^2) -(3600x) + 18000, and s and x are both in thousands of dollars.

a. Find the value of x that maximizes the rate of change of sales.
b. What is the significance of the value of x in (a)?

a. Revenue = sales
Rate of change = R'(x)

s(x) = (-3x^3) + (270x^2) -(3600x) + 18000
s'(x) = -9x^2 + 540x - 3600

Using the qaratic formula to determine s'(x) = 0 when x = 45

When x = 45 it maximizes the rate of change of sales

b. When $45000 is spent on advertising the maximum rate in sales occurs.

Thanks Sophie

 

[morson]

s(x) = (-3x^3) + (250x^2) -(3600x) + 18000
s'(x) = -9x^2 + 540x - 3600

There's your mistake.

 

[Sophie]

Morson

Thanks, that was silly, it was another typo.

Does your response mean I have interpreted the question correctly.

Sophie

 

[morson]

You interpreted the question correctly, albeit the little mistake led to incorrect answers on both questions. But, all that matters is that you understand it.

 

[Sophie]

Thanks for your time

It is very satisfying to know I am interpreting the written questions.

Sophie