Expert: Ahmed Salami - 10/22/2008

Question
need some help minimizing this equation...


(58+Rpi)(500000/pi)(r^-1)+19*pi*r^2

where R is a constant.


So far I have found the derivative to equal...

(58+R*pi)(-500000/(pi*r^2))+38pi*r

I know next I need to set the derivative equal to zero and solve for r. then plug it back into the original equation. but I am having a hard time after finding the derivative.

Answer
Hi Bobby,
Its really good that you've made some effort and so i'll just be
guiding you to the right path from here.
Let y be the function of r, then what we have now is of the form
dy/dr = a/r^2 + br
equating this to zero gives us
a/r^2 + br = 0
a/r^2 = -br
a = -br^3
r^3 = -a/b
In your case, writing pi as #
a = (58 + #R)(-500000/#)
 = -500000(58/# + R)
 = -29000000/#  -  500000R  
b = 38#

r^3 = (-29000000/#  -  500000R) / 38#
r is the cube root of all that.
I'm sure you can manage from here, but please get back to me if
there's any problem.
Regards.