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AP Calculus Exam Review Flashcards

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9845129170d/dx [ f(x) * g(x) ]f(x)*g'(x) + g(x)*f'(x)0
9845161145d/dx [ f(x) / g(x) ][ g(x) * f'(x) - f(x)* g'(x) ] / [ g(x) ]^21
9845163022d/dx f[ g(x) ]f'[ g(x) ] * g'(x)2
9845173145d/dx sin xcos x3
9845173875d/dx cos x-sin x4
9845174721d/dx tan xsec^2(x)5
9845176340d/dx cot x-csc^2(x)6
9845179908d/dx sec xsec x tan x7
9845181052d/dx csc x-csc x cot x8
9845183167d/dx e^xe^x9
9845184498d/dx ln x1/x10
9845190618L'Hopital's Rule11
9845192678ContinuityLimit from the left = Limit from the right = Function value12
9845205842Critical NumbersOccur where f'(x) = 0 or f'(x) DNE (denominator = 0)13
9845212914POSSIBLE Points of InflectionOccur where f''(x) = 0 or f''(x) DNE (denominator = 0)14
9845213959Points of InflectionOccur where f''(x) has a sign change15
9845219022Extreme Value TheoremAbsolute/Global extrema on a closed interval must occur either at a critical number or at endpoints16
9845225127Relative/Local Maximum (First Derivative Test)Occurs where f' changes from positive to negative17
9845227660Relative/Local Minimum (First Derivative Test)Occurs where f' changes from negative to positive18
9845232720Relative/Local Maximum (Second Derivative Test)Occurs when f''(critical number) < 019
9845241819Relative/Local Minimum (Second Derivative Test)Occurs when f''(critical number) > 020
9845245263Local Linear Approximationy - y1 = m ( x - x1) (Equation of a Tangent Line)21
9845249171Fundamental Theorem of Calculus22
9845254381Second Fundamental Theorem of Calculus23
9845263310Mean Value Theorem24
9845269381Average Value of a Function25
9845272308Intermediate Value Theorem26

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