Oxford University MAT 2015 Solved Papers

Sketching the three equations suggests the answer 7 , however it is necessary to note the behaviour of the three equations when $0\le \mathit{x}\le 1$. All three equations pass through 0 , and ${\mathit{x}}^5>{\mathit{x}}^4>{\mathit{x}}^3$ when $\mathit{x}>1$. When $0\le \mathit{x}\le 1$ it should be noted that ${\mathit{x}}^3\ge \mathit{s}\mathit{l}\mathit{a}\mathit{n}\mathit{t}{\mathit{x}}^4\ge \mathit{s}\mathit{l}\mathit{a}\mathit{n}\mathit{t}{\mathit{x}}^5$ and that all three equations pass through $\left(1,1\right)$. This behaviour produces two further regions (in addition to the 7 already discussed), and as such the answer is $\left(\mathit{d}\right)$.