20N.2.SL.TZ0.S_1

pestleMathematicsAISLPaper 220N· sl-2-4-key-features-of-graphs-intersections-using-technologysource ↗

Consider the function $f (x) = x^{2} + x + \frac{50}{x}, x \neq 0 .$

Find $f (1)$ .

[2]

Solve $f (x) = 0$ .

[2]

The graph of $f$ has a local minimum at point $A$ .

Find the coordinates of $A$ .

[2]

Markscheme / solution

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

attempt to substitute $x = 1$ (M1)

eg $f (1), 1^{2} + 1 + \frac{50}{1}$

$52$ (exact) A1 N2

[2 marks]

$- 4.04932$

$- 4.05$ A2 N2

[2 marks]

$(2.76649, 28.4934)$

$A (2.77, 28.5)$ A1A1 N2

[2 marks]

Examiners’ report

[N/A]