ohmymaths
- Mar 22, 2021
- 1 min read

Differentiation: Stationary Points Example 2

Question:

A rectangular sheet of metal measuring 120mm by 75mm has equal squares of side 𝑥 cut from each of the corners. The remaining flaps are then folded up to form an open box. Prove that the volume of the box is given by:

Answer:

Find the maximum volume of the box and the corresponding value of 𝑥.

To determine which value of x will produce the maximum volume, firstly find the second derivative:

Sub in x = 15:

As x = 15 will produce the maximum volume of the box, substitute x = 15 into original equation:

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