1st and 2nd Derivative Test

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Hint

f is increasing

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10 Terms

1

f is increasing

f’ +

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2

f is decreasing

f’ -

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3

f is concave up

f’’ +

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4

f is concave down

f’’ -

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5

Horizontal Tangent Line or Sharp Turn

f’ = 0 or f’ DNE

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6

The point that f changes concavity

f’’ = 0 or DNE AND f’’ changes signs

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7

1st derivative definition of the relative max of f (mountain)

f’ = 0 or DNE AND f’ changes sign from + to -

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8

1st derivative definition of the relative min of f (valley)

f’ = 0 or DNE AND f’ changes signs from - to +

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9

2nd derivative definition of the relative max of f (mountain)

f’ = 0 or DNE AND f’’ -

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10

2nd derivative definition of the relative min of f (valley)

f’ = 0 or DNE AND f’’ +

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