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Stationary points & Increasing/Decreasing Regions
Example:
Therefore, f(x) is:
Decreasing for x<−23
Stationary for x=−23
Increasing for x>−23
Inflexion points
Inflexion points occur when f′′(x)=0 and f′′(x) changes sign. 🚫
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Example:
f′′(x)=6x changes sign from − to + at x=0, so there is an inflexion point at x=0.
Graphs of f, f' and f''
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When f′ crosses the x-axis f has a maximum or minimum
When f′′ crosses the x-axis, f has an inflexion point.
Maxima & Minima
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Example:
So f′(x)=0 when x=0 or x=2.
Concavity
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