Types of Critical Points for f'(x)

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for when f'(x) = 0 or when f'(x) does not exist

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8 Terms

1
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Local Maximum (with Horizontal Tangent)
Local Maximum (with Horizontal Tangent)
2
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Local Minimum (with Horizontal Tangent)
Local Minimum (with Horizontal Tangent)
3
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Point of Inflection (Increasing, Horizontal Tangent)
Point of Inflection (Increasing, Horizontal Tangent)
4
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Point of Inflection (Decreasing, Horizontal Tangent)
Point of Inflection (Decreasing, Horizontal Tangent)
5
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Cusp (a local maximum with undefined tangent)
Cusp (a local maximum with undefined tangent)
6
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Cusp (a local minimum with undefined tangent)
Cusp (a local minimum with undefined tangent)
7
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Point of Inflection (Increasing, Vertical Tangent)
Point of Inflection (Increasing, Vertical Tangent)
8
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Point of Inflection (Decreasing, Vertical Tangent)
Point of Inflection (Decreasing, Vertical Tangent)