20N.1.SL.TZ0.T_13

pestleMathematicsAISLPaper 120N· sl-5-3-differentiating-polynomials-n-e-zsource ↗

Consider the graph of the function $f (x) = x^{2} - \frac{k}{x}$ .

The equation of the tangent to the graph of $y = f (x)$ at $x = - 2$ is $2 y = 4 - 5 x$ .

Write down $f' (x)$ .

[3]

Write down the gradient of this tangent.

[1]

Find the value of $k$ .

[2]

Markscheme / solution

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

$2 x + \frac{k}{x^{2}}$ (A1)(A1)(A1) (C3)

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

[3 marks]

$- 2.5 (\frac{- 5}{2})$ (A1) (C1)

[1 mark]

$- 2.5 = 2 \times (- 2) + \frac{k}{{(- 2)}^{2}}$ (M1)

Note: Award (M1) for equating their gradient from part (b) to their substituted derivative from part (a).

$(k =) 6$ (A1)(ft) (C2)

Note: Follow through from parts (a) and (b).

[2 marks]

Examiners’ report

[N/A]