## Applications of derivatives: extreme values

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?