1. ## Maximum and minimum

Hi,

Im doing a differentiation problem and somewhere i am going wrong so I am just going to type out my work and see if anyone can help

Surface are of cylinder is 60cm and we need to find the maximum and minimum volume

2pi r(h+r)=60
h+r= 60/2pi r
h+r=30/ pi r
h= (30/pi r) -r
h= (30-pi r^2)/ pi r)

placing h into volume formula

v= pi r^2*h

substituting h leaves -pi r^3+30r

dr/dv= -3r^2+30r=0
3r(-r+10)
r=10

where do i go from here.

how do i find the maximum and minimum??

2. Originally Posted by nikki1234
substituting h leaves -pi r^3+30r

dr/dv= -3r^2+30r=0
Hi

dv/dr = -3pi r^2+30
the extrema are found when dv/dr=0 ==> r=sqrt(10/pi)

3. Hi

Yes Ive done that and ive got two answers. one being positive and one being negative. Im assuming the positive is the maximum volume. For the minimum do I try and find a solution nearest to 0 or do i differentiate again?

4. For the minimum volume, you need first to determine the lowest and the highest possible value for r