1st and 2nd Derivative Test
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10 Terms
1
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f is increasing
f’ +
2
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f is decreasing
f’ -
3
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f is concave up
f’’ +
4
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f is concave down
f’’ -
5
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Horizontal Tangent Line or Sharp Turn
f’ = 0 or f’ DNE
6
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The point that f changes concavity
f’’ = 0 or DNE AND f’’ changes signs
7
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1st derivative definition of the relative max of f (mountain)
f’ = 0 or DNE AND f’ changes sign from + to -
8
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1st derivative definition of the relative min of f (valley)
f’ = 0 or DNE AND f’ changes signs from - to +
9
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2nd derivative definition of the relative max of f (mountain)
f’ = 0 or DNE AND f’’ -
10
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2nd derivative definition of the relative min of f (valley)
f’ = 0 or DNE AND f’’ +