Write down the derivative of $f$.

Find the point on the graph of $f$ at which the gradient of the tangent is equal to 6.

$12{x^2} - \frac{6}{{{x^3}}}$ or equivalent     (A1)(A1)(A1)     (C3)

Note:     Award (A1) for $12{x^2}$, (A1) for $- 6$ and (A1) for $\frac{1}{{{x^3}}}$ or ${x^{ - 3}}$. Award at most (A1)(A1)(A0) if additional terms seen.

[3 marks]

$12{x^2} - \frac{6}{{{x^3}}} = 6$     (M1)

Note:     Award (M1) for equating their derivative to 6.

$(1,{\text{ }}4)$$\,\,\,$OR$\,\,\,$$x = 1,{\text{ }}y = 4$     (A1)(ft)(A1)(ft)     (C3)

Note:     A frequent wrong answer seen in scripts is $(1,{\text{ }}6)$ for this answer with correct working award (M1)(A0)(A1) and if there is no working award (C1).

[3 marks]