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Date	May 2019	Marks available	2	Reference code	19M.2.SL.TZ1.S_3
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 1
Command term	Find	Question number	S_3	Adapted from	N/A

Question

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

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]

Syllabus sections

Topic 4—Statistics and probability » SL 4.1—Concepts, reliability and sampling techniques

Show 29 related questions

EXM.1.SL.TZ0.2c:
Give an example of a set of data with 7 numbers in it that does have an outlier, justify this fact by stating the Interquartile Range.
EXM.2.SL.TZ0.1c:
State the name for this type of sampling technique.
EXM.2.SL.TZ0.1a:
State the name for this type of sampling technique.
EXM.2.SL.TZ0.1d.i:
Calculate Pearson’s product moment correlation coefficient, $r$ .
18M.1.SL.TZ1.S_2a:
Find the value of the interquartile range.
17M.2.SL.TZ1.S_1b.i:
Find the mean.
17M.2.SL.TZ2.S_8b.i:
Write down the coordinates of A.
17M.2.SL.TZ2.S_8c.i:
Find the coordinates of B.
EXM.2.SL.TZ0.1b.i:
Show that 3 students will be selected from grade 12.
EXM.2.SL.TZ0.1d.iii:
Explain why the value of $r$ makes it appropriate to find the equation of a regression line.
EXM.2.SL.TZ0.1b.ii:
Calculate the number of students in each grade in the sample.
EXM.1.SL.TZ0.2b:
Hence, show that a data set with only 5 numbers in it cannot have any outliers.
17M.2.SL.TZ2.S_8b.ii:
Write down the rate of change of $f$ at A.
EXM.2.SL.TZ0.1d.ii:
Interpret the meaning of the value of $r$ in the context of the principal’s concerns.
EXM.1.SL.TZ0.2a:
Recalling definitions, such as the Lower Quartile is the $\frac{{n + 1}}{4}th$ piece of data with the data placed in order, find an expression for the Interquartile Range.
17M.2.SL.TZ2.S_8a:
Find the value of $p$ .
17M.2.SL.TZ2.S_8d:
Let $R$ be the region enclosed by the graph of $f$ , the $x$ -axis, the line $x = b$ and the line $x = a$ . The region $R$ is rotated 360° about the $x$ -axis. Find the volume of the solid formed.
17M.2.SL.TZ1.S_1a.ii:
Find the value of the range.
22M.2.SL.TZ2.5b:
Verify that the measurement of $0.46$ seconds is not an outlier.
17M.2.SL.TZ1.S_1a.i:
Write down the mode.
21M.1.SL.TZ1.4b:
Hence, find the minimum possible value of $L$ .
18M.1.SL.TZ1.S_2b:
One student sent k text messages, where k > 11 . Given that k is an outlier, find the least value of k.
17M.2.SL.TZ2.S_8c.ii:
Find the the rate of change of $f$ at B.
21M.1.SL.TZ2.7e.i:
Explain why this sampling method might not provide an accurate representation of the amount of time all of the students in the school spend doing homework.
21M.1.SL.TZ2.7e.ii:
Suggest a more appropriate sampling method.
EXM.2.SL.TZ0.1e:
Another student at the school, Jasmine, has a self-esteem value of 29.

By finding the equation of an appropriate regression line, estimate the time Jasmine spent on social media the previous day.
21M.1.SL.TZ1.4a:
Find the minimum possible value of $U$ .
22M.1.SL.TZ1.3a:
Find the largest value of $c$ that would not be considered an outlier.
17M.2.SL.TZ1.S_1b.ii:
Find the variance.

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