Moderate -0.8 This is a straightforward application of differentiation to prove monotonicity. Students need to find f'(x) using the chain rule, then show f'(x) > 0 for all x. The algebra is simple: f'(x) = 6(2x-5)² + 1, which is clearly always positive since it's a square term plus 1. This is easier than average as it requires only one standard technique with no problem-solving insight.
1 It is given that $\mathrm { f } ( x ) = ( 2 x - 5 ) ^ { 3 } + x$, for $x \in \mathbb { R }$. Show that f is an increasing function.
\hfill \mbox{\textit{CAIE P1 2013 Q1 [3]}}