Standard +0.3 This is a standard calculus application requiring differentiation of a cubic, setting f'(x) > 0, and solving a quadratic inequality. While it involves multiple steps (differentiate, factorise/solve quadratic, determine sign), these are routine A-level techniques with no novel insight required, making it slightly easier than average.
For an increasing function \(x < -\frac{2}{3}\) or \(x > 4\)
A2
AO2 (f.t. candidate's derived two critical values for \(x\))
Deduct 1 mark for each of the following errors: the use of non-strict inequalities; the use of the word 'and' instead of the word 'or'
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Total: [5]
$f'(x) = 3x^2 – 10x – 8$ | M1 | AO1 (At least one non-zero term correct)
Critical values $x = -\frac{2}{3}$, $x = 4$ | A1 | AO1 (c.a.o.)
For an increasing function, $f'(x) > 0$ | m1 | AO1
For an increasing function $x < -\frac{2}{3}$ or $x > 4$ | A2 | AO2 (f.t. candidate's derived two critical values for $x$)
Deduct 1 mark for each of the following errors: the use of non-strict inequalities; the use of the word 'and' instead of the word 'or' | — | —
**Total: [5]**
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Find the range of values of $x$ for which the function
$$f(x) = x^3 - 5x^2 - 8x + 13$$
is an increasing function. [5]
\hfill \mbox{\textit{WJEC Unit 1 Q16 [5]}}