17N.1.SL.TZ0.T_14

pestleMathematicsAISLPaper 117N· sl-5-1-introduction-of-differential-calculussource ↗

A function $f$ is given by $f(x) = 4{x^3} + \frac{3}{{{x^2}}} - 3,{\text{ }}x \ne 0$ .

Write down the derivative of $f$ .

[3]

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

[3]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$12{x^2} - \frac{6}{{{x^3}}}$ 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]

Examiners’ report

[N/A]