21M.2.SL.TZ2.2

pestleMathematicsAASLPaper 221M· sl-2-4-key-features-of-graphs-intersections-using-technologysource ↗

Let $f (x) = 3 x - 4^{0.15 x^{2}}$ for $0 \leq x \leq 3$ .

Sketch the graph of $f$ on the grid below.

[3]

Find the value of $x$ for which $f' (x) = 0$ .

[2]

Markscheme / solution

A1A1A1

Note: Award A1 for a smooth concave down curve with generally correct shape. If first mark is awarded, award A1 for local maximum and $x$ -intercept in approximately correct position, award A1 for endpoints at $x = 0$ and $x = 3$ with approximately correct $y$ -coordinates.

[3 marks]

recognizing that $f' (x) = 0$ at local maximum (M1)

$x = 2.33084 \dots$

$x = 2.33$ A1

[2 marks]

Examiners’ report

[N/A]