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9 marksDifferentiation I

CAPE Pure Mathematics Unit 1 · May/June 2023 · Paper 2 · Question 5(c)(ii)

A container in the shape of an open-top cuboid is made from a sheet of metal of length 16 m and width 13 m by cutting squares of side length x m from each corner.

Using the method of the second derivative, determine the height, x, that will maximize the volume of the container.

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Other parts of this question

  1. 5(a)Determine \lim_{x \to \infty} \frac{2x^3 - 4x + 1}{3x^4 + x^2 - 2}.[5 marks]
  2. 5(b)How fast is the water in the cup rising when the height is 4 cm?[8 marks]
  3. 5(c)(i)Show that the volume of the container is 4x^3 - 58x^2 + 208x.[2 marks]
  4. 5(c)(iii)Determine the maximum volume of the container.[1 mark]

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