Question

Calculus :Find the number of unit x that produces a maxima revenue R.
R=228x^2 - 0.08x^3
x= ? units

Answer 1

Are you taking Calculus?

Answer 2

yes

Answer 3

OK, for Calculus questions, I suggest you mark your questions as Calculus and you get a better response from the experts. I should let them answer Calculus questions, but I believe all you need to do it the following.

Take the first derivative of your equation. You will get a quadratic equation which you can solve for x using the quadratic equation formula. This will get you x values for the maximum and minimum values that you are seeking. Plug the x value back into your original equation to find the y value or R value in your case.

Also, I suggest you use the equation editor by immediately replying to your question and clicking on the equation button.

Answer 4

You can also ping one of the experts. Unfortunately, I don't know how to do it.

Answer 5

Thank you ill edit my question so people know its calculus.

Answer 6

Hello?

Answer 7

Do you still need help?

Answer 8

hi can you help me with this problem?

Answer 9

I agree with marchall in taking the first derivative. Have you done that?

Answer 10

Have you learned power rule? Or are you just allowed to use the definition of derivative to find the derivative?

Answer 11

i got \[456x-0.24x^2\]

Answer 12

Now you want to find the critical numbers.

Answer 13

i learned how to find it by using the second derivative test and finding critical numbers

Answer 14

That means we need find when that is zero.

Answer 15

You can factor your expression.

Answer 16

There is common factor x in both terms.

Answer 17

i g0t 1900=x

Answer 18

and x=0

Answer 19

Those critical numbers look great.

Answer 20

Now as you suggested we can determine if those numbers will give us a max or a min.

Answer 21

By finding second derivative.

Answer 22

second derivative is 456-0.48x

Answer 23

\[f''(x)=456-0.48x \\ f''(0)=456>0 \\ f''(1900)=-456<0\]

Answer 24

So when f'' >0 we have what?
and when f''<0 we have?

Answer 25

I like to go back to a real basic graph to help me remember. f(x)=x^2 has a min and f''>0 and if f(x)=-x^2 then f has a max and f''<0

Answer 26

f''>0 min, f''<0 max

Answer 27

yes exactly

Answer 28

Thank you so much ! this really helped a lot!

Answer 29

You did all the work jackie. I think you know more than you think you do.