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Maths (A-Level Revision) Pure Mathematics Calculus Differentiation Stationary Points Quick revise Increasing and Decreasing Functions An increasing function is a function where: if x 1 > x 2, then f (x 1) > f (x 2) , so as x increases, f (x) increases. A decreasing function is a function which decreases as x increases.

A stationary point can be: - A local maximum, where the gradient changes from positive to negative (+ to -) - A local minimum, where the gradient changes from negative to positive (- to +) - A stationary point of inflection, where the gradient has the same sign on both sides of the stationary point

Finding the Nature of Stationary Points. Once we’ve found our stationary points, we need to find out whether they are a maximum, minimum, or a stationary point of inflection. We do this by differentiating our derivative again. So, for example, take our first example of y = x^2 - 1. We said that \dfrac {dy} {dx} = 2x.

Stationary Points. Examples, videos, activities, solutions, and worksheets that are suitable for A Level Maths to help students learn how to find stationary points by differentiation. The following diagram shows stationary points and inflexion points. Scroll down the page for more examples and solutions for stationary points and inflexion points.

Stationary points are points on a graph where the gradient is zero. There are three types of stationary points: maximums, minimums and points of inflection (/inflexion). The three are illustrated here: Example. Find the coordinates of the stationary points on the graph y = x 2. We know that at stationary points, dy/dx = 0 (since the gradient is ...

What are stationary points? · A stationary point is any point on a curve where the gradient is zero · To find stationary points of a function f(x) Step 1: Find ...

Stationary Points When \dfrac {df (x)} {dx}>0, the function f (x) is increasing. When \dfrac {df (x)} {dx}<0, the function f (x) is decreasing. A stationary point of a function is when it is neither increasing – i.e. when \dfrac {df (x)} {dx}=0 Make sure you are happy with the following topics before continuing. Differentiation

and substitute each value of x to find the kind of stationary point(s). (+ suggests a minimum, – a maximum, ... Advanced Level, Modelling with calculus.

To find stationary points of a function f (x) Step 1: Find the first derivative f' (x) Step 2: Solve f' (x) = 0 to find the x -coordinates of the stationary points. Step 3: Substitute those x -coordinates into f (x) to find the corresponding y -coordinates. A stationary point may be either a local minimum, a local maximum, or a point of inflection.

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Stationary points (or turning/critical points) are the points on a curve where the gradient is 0. This means that at these points the curve is flat.

Stationary Points - What are they? In the first of these videos I explain what we mean by stationary points and the different types of stationary points you can have. Finding Stationary Points - Example

Stationary Points | Edexcel A Level Maths Pure Revision Notes 7.2.4 Stationary Points & Turning Points What are stationary points? A stationary point is any point on a curve where the gradient is zero To find stationary points of a function f (x) Step 1: Find the first derivative f' (x)

Find the coordinates of the stationary points on the graph y = x2 . We know that at stationary points, dy/dx = 0 (since the gradient is zero at stationary ...

The second derivative test is used to determine whether a stationary point is a local maximum or minimum. A stationary point x x is classified based on whether ...

Stationary Points - What are they? In the first of these videos I explain what we mean by stationary points and the different types of stationary points you can have. Finding Stationary Points - Example

Stationary Points. Examples, videos, activities, solutions, and worksheets that are suitable for A Level Maths to help students learn how to find stationary points by differentiation. The following diagram shows stationary points and inflexion points. Scroll down the page for more examples and solutions for stationary points and inflexion points.