Applications of derivatives: extreme values
Task number: 3021
Using derivatives, determine:
Variant 1
Which retangle with perimeter \(\ell\) has the greatest area?
Variant 2
Which cylinder with volume \(V\) has the smallest surface area?
Variant 3
We cut out small squares from the corners of a square sheet of paper and fold it to make a box (without a lid). How large should the cut-out squares be to maximize the volume of the box that is formed?
