Derivative Tests

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10 Terms

1
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First Derivative Test

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Relative minimum

when f’(x) is negative before the 0 and positive after the 0

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Relative maximum

when f’(x) is positive before the 0 and negative after the 0

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Critical Points

where f’(x) = 0 or undefined

5
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Double Angle Sin

2sin(x)cos(x)

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Double Angle Cos

cos²(x) - sin²(x)

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Second Derivative Test

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Local Max

f’(x) = 0 and f’’(x) < 0


Concave down

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Local Minimum

f’(x) = 0 and f’’(x) > 0


Concave up

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Inflection Point

when f’’(x) changes sign


when f’’(x) = 0 or is undefined and is concave up on one side and concave down on the other