Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability (resit) / 6 / b / i

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- Solution i

Solution

The derivative factors as

g^{'} (x) = 4 x^{3} - 24 x^{2} + 36 x = 4 x (x - 3)^{2} .

The polynomial is differentiable everywhere, so its critical points occur precisely where this derivative vanishes. Hence

x = 0 and x = 3.

Their values are

g (0) = 5

and

g (3) = 32

.

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