Standard +0.3 This is a straightforward application of differentiation to determine monotonicity. Students need to find f'(x) using quotient/chain rule and power rule, then analyze its sign over the given domain x < -1. The algebra is routine and the domain restriction makes sign analysis simpler than average, placing this slightly above trivial but easier than a typical A-level question.
1 The function f is defined by \(\mathrm { f } ( x ) = \frac { 1 } { 3 x + 2 } + x ^ { 2 }\) for \(x < - 1\).
Determine whether f is an increasing function, a decreasing function or neither.
1 The function f is defined by $\mathrm { f } ( x ) = \frac { 1 } { 3 x + 2 } + x ^ { 2 }$ for $x < - 1$.\\
Determine whether f is an increasing function, a decreasing function or neither.\\
\hfill \mbox{\textit{CAIE P1 2020 Q1 [3]}}