Question

The unit price of x units of a certain product is given by P(x)=(450/x+3)-3. What is the maximum possible revenue when selling x units?

Answer 1

Is this a calculus problem?

Answer 2

\[
P(x) = \frac{450}{x+3}-3
\]

Answer 3

yes

Answer 4

Is it a calculus class?

Answer 5

yes

Answer 6

Find the derivative first.

Answer 7

I found it and got about $332, but I'm not sure.

Answer 8

Did you get the derivative?

Answer 9

Yes, -450/(x+3)^2

Answer 10

The maximum revenue from selling x units is required. Let the revenue be R. To find the revenue from selling x units, we need to multiply the unit price by x, giving:
\[\large R(x)=\frac{450x}{x+3}-3x\ .........(1)\]
Are you with me so far?

Answer 11

@kperez128 Are you there?

Answer 12

yes, I did that

Answer 13

Now you need find dR/dx. If you have done that what was your result?

Answer 14

\[\frac{ 450x}{x+3^{2} }+\frac{ 450 }{ x+3}-3\]

Answer 15

My result of the differentiation of (1) with respect to x is as follows:
\[\large \frac{dR}{dx}=\frac{450(x+3)-450x}{(x+3)^{2}}-3\ .........(2)\]

Answer 16

@kperez128 Are you checking your differentiation?