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Card 12 / 14:
first derivative test
let f be a continuous function over an interval I containing a critical point c such that f is differentiable over I except possibly at c ; if f ′ changes sign from positive to negative as x increases through c , then f has a local maximum at c ; if f ′ changes sign from negative to positive as x increases through c , then f has a local minimum at c ; if f ′ does not change sign as x increases through c , then f does not have a local extremum at c
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