19M.2.SL.TZ1.S_3

pestleMathematicsAASLPaper 219M· sl-4-1-concepts-reliability-and-sampling-techniquessource ↗

Consider the function $f\left( x \right) = {x^2}{{\text{e}}^{3x}}$ , $x \in \mathbb{R}$ .

The graph of $f$ has a horizontal tangent line at $x = 0$ and at $x = a$ . Find $a$ .

Markscheme / solution

valid method (M1)

eg $f'\left( x \right) = 0$ , ,

$a = - 0.667\left( { = - \frac{2}{3}} \right)$ (accept $x = - 0.667$ ) A1 N2

[2 marks]

Examiners’ report

[N/A]