 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-1/16/f/solution

F (2/3) = 4 (\frac{2}{3})^{3} - 3 (\frac{2}{3})^{4} = \frac{16}{27} > \frac{1}{2} .

Since

F

is strictly increasing on

(0, 1)

, its unique crossing of

1/2

occurs earlier. Therefore the median is less than the mode.

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