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?

Difficulty level: Easy task (using definitions and simple reasoning)
Solution require uncommon idea
Cs translation
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