Methods2026 NHT Exam 1 · Q7Tech-free3 marks

Maximising the area of an inscribed rectangle

Let $f:(0, 12) \to R,\ f(x) = \sqrt{12 - x}$ .

Show that the area of the rectangle can be expressed as $A(k) = \sqrt{12k^2 - k^3}$ .

1 mark

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Determine the value of $k$ that maximises the area of the rectangle.

2 marks

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