14G - The nature of stationary points
14G - Content video: The nature of stationary points
This video covers the theory and an example of how to determine the nature of stationary points for a graph.
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A stationary point occurs when the gradient of a tangent line to a curve is zero.
- To find the \(x\)-ordinate of a stationary point on the curve of \(f(x)\), solve \(f'(x)=0\) for \(x\).
- To find the \(y\)-ordinate of a stationary point, subsitute the \(x\)-value into the original function, \(f(x)\).
Types of stationary points
There are three types of stationary points:
Determining the nature of a stationary point
They nature of a stationary point can be determined using any of the three methods below:
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14G - Example 1: Determining the nature of stationary points using a "sign" diagram
Determine the nature of the stationary points for the function \(y=2x^3-12x^2+24x-13\).
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14G - Example 1: Video solution
14D - Example 1: Practice
Question 1: Determine the nature of the stationary points for the graph of \(f(x)=x^3-3x^2-9x-5\). Question 2: Determine the nature of the stationary points for the graph of \(y=-x^4+4x^2\). Question 3: Determine the nature of the stationary points for the graph of \(g(x)=x^4-6x^2+8x-3\). 14D - Example 1: Solutions
Question 1:
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