Moderate -0.5 This is a straightforward application of the condition for an increasing function (dy/dx > 0), requiring students to solve a simple quadratic inequality. The algebraic manipulation is routine for C2 level, involving factorising x(x-6) > 0 and identifying x < 0 or x > 6. While it tests understanding of the connection between gradient and increasing functions, it requires no novel insight and fewer steps than a typical multi-part question.
The gradient of a curve is given by \(\frac{dy}{dx} = x^2 - 6x\). Find the set of values of \(x\) for which \(y\) is an increasing function of \(x\). [3]
Question 10:
10 | x < 0 and x > 6 | 3 | B2 for one of these or for 0 and 6
identified or M1 for x2 -6x > 0 seen
(M1 if y found correctly and sketch
drawn) | 3
The gradient of a curve is given by $\frac{dy}{dx} = x^2 - 6x$. Find the set of values of $x$ for which $y$ is an increasing function of $x$. [3]
\hfill \mbox{\textit{OCR MEI C2 Q10 [3]}}