Calculus paper with derivative. Please help!

[paradise]

Hi there, so here is the problem
A solf drink company wishes to design a cylindrical aluminum container in which they can sell 12 ounce portions of their product. This company, naturally concerned about evironment issues, wishes to use the lease amount of alumium possible. What dimesion should the can be?Justify your answer by including a graph of the function for x>0, find the first derivative and the critical value for the radium for x>0, find the second derivative and show that the function has the appropriate concavity at that critical value
Given: volume from a coke can is 355 ml

so i got start by
355=pi r^2
h= 355 / pi r ^2

so Surface Area is: 2pi r h+ 2 pi r^2
equation: SA= 2 pi r^2+710 r^-1
1st Derivative: 4pi r - 710

and then to find the critical value i se the first derivative to equal 0 and the critical poin of the first derivative is (177.5 / pi, 20070.0681). Then i tried to graph the original equation but instead of a parabola i got something really weird. DId i mess up on anything?please help! and what should i do next?thank you so much!

 

[tkhunny]

1) Why are you expecting a parabola?
2) This thing has practical Domain limitations. r > 0. That would make for a rather abrupt end to your parabola.
3) When you solved for "h", you managed r^2 in the denominator. This could lead to a vertical asymptote.
4) SA(r) is perfect. Go with that.
5) SA'(r) is no good. You got the first part. No so much on the 710-section. Why did you INCREASE the exponent? Shouldn't it decrease by 1? -1 - 1 = -2.

Good work getting this far. Just fix the details and you're done.