Moderate -0.8 This is a straightforward application of basic differentiation (power rule) followed by solving a quadratic inequality. Both are routine C2 skills with no problem-solving insight required, making it easier than average but not trivial since it requires correct inequality reasoning.
Answer: \(6x^2 + 18x - 24\); their \(6x^2 + 18x - 24 = 0\) or \(> 0\) or \(\ge 0\); \(-4\) and \(+1\) identified oe; \(x < -4\) and \(x > 1\) cao
Answer
Marks
Guidance
Marks: B1
M1
A1
Guidance: or sketch of \(y = 6x^2 + 18x - 24\) with attempt to find \(x\)-intercepts; or \(x \le -4\) and \(x \ge 1\); if B0M0 then SC2 for fully correct answer
**Answer:** $6x^2 + 18x - 24$; their $6x^2 + 18x - 24 = 0$ or $> 0$ or $\ge 0$; $-4$ and $+1$ identified oe; $x < -4$ and $x > 1$ cao
**Marks:** B1 | M1 | A1 | A1 | [4]
**Guidance:** or sketch of $y = 6x^2 + 18x - 24$ with attempt to find $x$-intercepts; or $x \le -4$ and $x \ge 1$; if B0M0 then SC2 for fully correct answer
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Differentiate $2x^3 + 9x^2 - 24x$. Hence find the set of values of $x$ for which the function $f(x) = 2x^3 + 9x^2 - 24x$ is increasing. [4]
\hfill \mbox{\textit{OCR MEI C2 2013 Q6 [4]}}