Moderate -0.8 This is a straightforward application of the standard rule that a function is increasing when dy/dx > 0. Students need only solve the quadratic inequality x² - 6x > 0 by factoring to x(x-6) > 0, giving x < 0 or x > 6. This requires basic algebraic manipulation with no conceptual difficulty or multi-step reasoning, making it easier than average.
7 The gradient of a curve is given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = x ^ { 2 } - 6 x\). Find the set of values of \(x\) for which \(y\) is an increasing function of \(x\).
7 The gradient of a curve is given by $\frac { \mathrm { d } y } { \mathrm {~d} x } = x ^ { 2 } - 6 x$. Find the set of values of $x$ for which $y$ is an increasing function of $x$.
\hfill \mbox{\textit{OCR MEI C2 2007 Q7 [3]}}