Standard +0.3 This is a straightforward application of differentiation to find where a function is increasing. Students need to find f'(x) = 3x² - 2x - 8, set it ≥ 0, solve the quadratic inequality, and identify the appropriate boundary. While it requires multiple steps (differentiate, factorize/solve quadratic, interpret inequality), these are all standard techniques with no novel insight required, making it slightly easier than average.
2 A function f is defined by \(\mathrm { f } : x \mapsto x ^ { 3 } - x ^ { 2 } - 8 x + 5\) for \(x < a\). It is given that f is an increasing function. Find the largest possible value of the constant \(a\).
2 A function f is defined by $\mathrm { f } : x \mapsto x ^ { 3 } - x ^ { 2 } - 8 x + 5$ for $x < a$. It is given that f is an increasing function. Find the largest possible value of the constant $a$.\\
\hfill \mbox{\textit{CAIE P1 2017 Q2 [4]}}