Question

The revenue derived from the production of x units of a particular commodity is:
R(x)= (35x-x^2)/(x^2+35) million dollars. What level of production results in maximum revenue? What is the maximum revenue?

Answer 1

I have the 1st derivative as (-4x^3+105x^2-70x+1225) / (x^2+35)^2
is this correct?

Answer 2

\[(x^2 +35)(35-2x) - (2x)(35x-x^2) // (x^2+35)^2\]

the "//" means "all over" (x^2+35)^2

Answer 3

-70x/(x^2+35)^2 is what I get...and im prone to error ;)

Answer 4

and I see an error....

Answer 5

\[35x^2 +35^2 -2x^3 -70x -70x^2 +2x^3\]

Answer 6

\[-35x^2 -70x +35^2\]

Answer 7

-35(x^2 +2x -35)//(x^2-35)^2

Answer 8

thats correct :)

Answer 9

now when (x^2 +2x -35) is equal to zero, youll have your answer I beleive

Answer 10

(x+7)(x-5)

x = -7 or x=5 take your pick ;)

Answer 11

ok I got lost back at the begining. After the quotient rule when I multiply I get \[-2x ^{3 } + 35x ^{2} - 70x +1225 - 70x ^{2} +2x ^{3} // (x ^{2} + 35)^{2}\]

Answer 12

never mind I see where we have the same. you just wrote it a little differently. the 35^2 instead of 1225.

Answer 13

yeah... I figured it be easier on me to not figure 35^2 out ...

Answer 14

925+150+150 = 925+300 = 1225

Answer 15

thats my georgia math :)

Answer 16

ok when you factor out the 35 should it be negative. \[-35(x ^{2} + 2x - 35) // (x ^{2}+35)^{2}\] I would have put 35(-x^2-2x+35) // (x^2+35)^2
I have to start a new post. When these get too long my computer goes REALLY SLOW

Answer 17

factor out the negative so you have a "normal" quadratic to play with..

Answer 18

same results, just easier to get to