IB Mathematics Applications & Interpretation Topic SL 5.2—increasing and Decreasing Functions Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 5.2—increasing and Decreasing Functions Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 5.2—increasing and Decreasing Functions with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 5.2—increasing and Decreasing Functions and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 2

A technology company is analyzing the performance of its new software product. Let $x$ be the number of months after launch, and let $f (x)$ be the profit in thousands of dollars. The function representing the profit from the software is given by:

$f (x) = 2 x^{3} - 9 x^{2} + 12 x + 1$

Find the derivative $f^{'} (x)$ .

[2]

Solve $f^{'} (x) = 0$ to find the critical points.

[3]

Determine the intervals where the function is increasing and decreasing.

[3]

Determine the $x$ -coordinates of the local maximum and minimum points.

[2]

Sketch the graph of the function, clearly labeling the critical points and behavior.

[3]

Question 2

SLPaper 2

Consider the function $g$ defined by $g (x) = x^{3} - 12 x + 1$ .

Find the derivative $g^{'} (x)$ .

[2]

Solve $g^{'} (x) = 0$ to find the critical points.

[3]

Determine the intervals where the function is increasing and decreasing.

[3]

Determine the $x$ -coordinates of the local maximum and minimum points.

[2]

Sketch the graph of the function, clearly labeling the critical points and behavior.

[3]

Question 3

SLPaper 2

A startup company is analyzing its profit growth over time to make strategic decisions. The rate at which the company's profit is changing over time is given by:

$\frac{d P}{d t} = 3 t^{2} - 8 t$

where $P$ represents the company's profit (in thousands of dollars), $t$ is the time in years since the company was founded ( $t \geq 0$ ), and $\frac{d P}{d t}$ is measured in thousands of dollars per year.

Find the values of $t$ ( $t \geq 0$ ) for which $\frac{d P}{d t} = 0$ .

[4]

Determine the intervals of time for which the profit is increasing and decreasing.

[4]

Interpret the meaning of these intervals in the context of the company's profit.

[3]

Question 4

SLPaper 1

During summer, a biologist records $T$ , the water temperature in $^{\circ}$ C, and $A$ , the area in m $^{2}$ covered by algae in a pond. She develops a mathematical model for her data, given by: $\frac{d A}{d T} = - 0.8 T + 20$ , $10 \leq T \leq 28$ .

State whether the function $A$ with respect to $T$ is increasing or decreasing at the point where $T = 2 6^{\circ}$ C. Show your reasoning.

[3]

It is known that when the water temperature is $1 0^{\circ}$ C, the area covered by algae is $170$ m $^{2}$ . Determine the general function $A (T)$ .

[5]

Question 5

SLPaper 2

A technology start-up is reviewing the earnings from a recently launched data-management tool. Let $x$ denote the number of months since the launch, and let $f (x)$ represent the profit, measured in thousands of dollars. The profit is modeled by:

$f (x) = 2 x^{3} - 33 x^{2} + 168 x + 10$

Find $f^{'} (x)$ for this function.

[2]

Solve $f^{'} (x) = 0$ to obtain the critical points.

[3]

Determine where the function is increasing and where it is decreasing.

[3]

Determine the $x$ -coordinates at which the local maximum and local minimum points occur.

[2]

Sketch the graph of the function, clearly marking the critical points and showing the behavior.

[3]

IB Mathematics Applications & Interpretation SL 5.2—increasing and Decreasing Functions Questionbank

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IB Mathematics Applications & Interpretation SL 5.2—increasing and Decreasing Functions Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 5.2—increasing and Decreasing Functions Questionbank

Unlock all 14 questions with a free account