Find the number of units x that produces a maximum revenue R.
R = 114x^2 − 0.04x^3
x = _______units

Question

Find the number of units x that produces a maximum revenue R.
R = 114x^2 − 0.04x^3
x =   _______units

anonymous · Answer

So far I have taken the 1st derivative and 2nd derivative I  have 
R'=228x-.12x^2
R" =228-.24x
Now I set R' to equal 0 which is R' 228x-.12^2=0
I'm not sure how to get the critical point?

anonymous · Answer

Somebody PLEASE help me??/

amilapsn · Answer

zeros of R' are the critical points...

anonymous · Answer

I dunno how to get the number for x.... it must be a large number because i can't figure out x...

amilapsn · Answer

Factorize R', then it's easy to figure out zeros...

anonymous · Answer

R' x(228-.12x)??? I don't see what x can be still

imstuck · Answer

What you have after you find your first derivative is 228x-.12x^2.

amilapsn · Answer

What are the x values in the critical points?

imstuck · Answer

in other words, you have this:$$R'=-.12x ^{2}+228x$$I would multiply by 100 to get rid of the decimal, like this:

amilapsn · Answer

They are the x values when R' = 0

imstuck · Answer

$$R'=-12x ^{2}+22800x$$Of course I would also switch the signs:$$R'=12x ^{2}-22800x$$Now factor out an x and get this:$$R'=x(12x-22800)$$x = 0 or 12x-22800=0.  12x=22800 and x = 1900

imstuck · Answer

x=1900 units.

anonymous · Answer

ok, that's what i was looking for IMSTUCK.. I understand how to do the whole problem except the whole - decimal number kept throwing me off. Thank you for the steps again though. I will keep that in mind when i have - decimal numbers

anonymous · Answer

all i have to do to check is plug 1900 in for x and i should get 0 :)