Given a function \(f(x)\) and its curve \(y=f(x)\), a stationary point (aka critical point) is a point along the curve at which:
\[f'(x)=0\]
Which can also be written:
\[\frac{dy}{dx} = 0\]
Consequently at a stationary point the curve's gradient is equal to zero and the tangent to the curve horizontal.
A stationary point can be either one of the following three types:
Now that we have defined what a stationary point is we learn how to locate them.
We start by summarizing the method, below, in two steps. We then illustrate this method with a tutorial.
To find the stationary point(s) of a curve, \(y=f(x)\), we need to determine the point(s) at which \(f'(x)=0\). We can summarize the method in two steps:
In the following tutorial we review the ... .
Using the method, described above, find the coordinates of any stationary points on each of the following curves: