Find range where function increasing/decreasing

A question is this type if and only if it asks to find the set of values of x (or range) for which a given function is increasing or decreasing, requiring solving an inequality involving the derivative.

30 questions · Moderate -0.4

1.07o Increasing/decreasing: functions using sign of dy/dx

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CAIE P1 2014 November Q6

6 marks Moderate -0.3

The equation of a curve is $y = x^3 + ax^2 + bx$, where $a$ and $b$ are constants.

In the case where the curve has no stationary point, show that $a^2 < 3b$. [3]
In the case where $a = -6$ and $b = 9$, find the set of values of $x$ for which $y$ is a decreasing function of $x$. [3]

CAIE P1 2016 November Q4

4 marks Standard +0.3

The function $f$ is such that $f(x) = x^3 - 3x^2 - 9x + 2$ for $x > n$, where $n$ is an integer. It is given that $f$ is an increasing function. Find the least possible value of $n$. [4]

OCR MEI C2 Q2

11 marks Moderate -0.3

Fig. 11 shows the curve $y = x^3 - 3x^2 - x + 3$. \includegraphics{figure_11}

Use calculus to find $\int_{-1}^{3} (x^3 - 3x^2 - x + 3) dx$ and state what this represents. [6]
Find the $x$-coordinates of the turning points of the curve $y = x^3 - 3x^2 - x + 3$, giving your answers in surd form. Hence state the set of values of $x$ for which $y = x^3 - 3x^2 - x + 3$ is a decreasing function. [5]

WJEC Unit 1 Specimen Q16

5 marks Standard +0.3

Find the range of values of $x$ for which the function $$f(x) = x^3 - 5x^2 - 8x + 13$$ is an increasing function. [5]

WJEC Unit 3 2024 June Q13

3 marks Standard +0.8

The diagram below shows a sketch of the graph of $y = f'(x)$ for the interval $[x_1, x_5]$. \includegraphics{figure_13}

Find the interval on which $f(x)$ is both decreasing and convex. Give reasons for your answer. [2]
Write down the $x$-coordinate of a point of inflection of the graph of $y = f(x)$. [1]