I am working on an optimization problem right now and ran into the following situation.
I think I have done this wrong, but I am fairly tired right now and can't seem to find my mistake.
Not sure where I got the idea that [LaTeX ERROR: Convert failed] .
Trying to minimize the surface area. However; I know how to solve the rest of the problem. Thanks for the help.
Edit: Actually, I got stuck again.
[LaTeX ERROR: Convert failed] [LaTeX ERROR: Convert failed]
[LaTeX ERROR: Convert failed]
[LaTeX ERROR: Convert failed]
[LaTeX ERROR: Convert failed]
[LaTeX ERROR: Convert failed]
Then solving for dA/dR = 0.
[LaTeX ERROR: Convert failed]
[LaTeX ERROR: Convert failed]
[LaTeX ERROR: Convert failed]
And from there I can't find a way to isolate R, probably because I made some silly algebraic error.
Hi Vanilla,
The volume of a cylinder is
The curved surface area is
The flat surface area is
The total surface area of a cylinder closed at both ends (surface area of a solid cylinder) is
Substitute the equation for H into A to get an equation for SA in terms of the single variable R...
Surface area
Differentiating with respect to R and setting derivative to zero
finds the value of R that gives minimum surface area.
Double check whether or not the cylinder is closed.
The cylinder is open on one end. So the [LaTeX ERROR: Convert failed] in the surface area equation would instead be , correct?
So differentiating [LaTeX ERROR: Convert failed] would still leave me with [LaTeX ERROR: Convert failed] for which I can't seem to isolate R when solving for 0.
I think I got it.
[LaTeX ERROR: Convert failed] can be simpified to [LaTeX ERROR: Convert failed] , which then differentiates to [LaTeX ERROR: Convert failed] . And for [LaTeX ERROR: Convert failed] , [LaTeX ERROR: Convert failed] . Thanks for the help!