Standard +0.3 This question requires students to find when f'(x) > 0 for an increasing function by factorizing a quadratic and solving an inequality. It's a straightforward application of the relationship between derivatives and increasing functions, requiring only factorization of x² - 6x + 8 = (x-2)(x-4) and identifying that f'(x) > 0 when x > 4, making n = 4. Slightly above average difficulty due to the need to connect multiple concepts (derivatives, increasing functions, inequalities) but still a standard textbook-style question.
2 An increasing function, f , is defined for \(x > n\), where \(n\) is an integer. It is given that \(\mathrm { f } ^ { \prime } ( x ) = x ^ { 2 } - 6 x + 8\). Find the least possible value of \(n\).
2 An increasing function, f , is defined for $x > n$, where $n$ is an integer. It is given that $\mathrm { f } ^ { \prime } ( x ) = x ^ { 2 } - 6 x + 8$. Find the least possible value of $n$.\\
\hfill \mbox{\textit{CAIE P1 2019 Q2 [3]}}