Moderate -0.8 This is a straightforward application of differentiation to prove monotonicity. Students need to find f'(x) = -3x^(-4) - 3x^2, factor out -3, and observe both terms are positive for x > 0, making f'(x) < 0. It's a direct single-method question with clear algebraic steps and no conceptual subtlety beyond the basic derivative test for decreasing functions.
2 It is given that $\mathrm { f } ( x ) = \frac { 1 } { x ^ { 3 } } - x ^ { 3 }$, for $x > 0$. Show that f is a decreasing function.
\hfill \mbox{\textit{CAIE P1 2012 Q2 [3]}}