AP Calculus Exam Review Flashcards

9845129170	d/dx [ f(x) * g(x) ]	f(x)g'(x) + g(x)f'(x)	0
9845161145	d/dx [ f(x) / g(x) ]	[ g(x) * f'(x) - f(x)* g'(x) ] / [ g(x) ]^2	1
9845163022	d/dx f[ g(x) ]	f'[ g(x) ] * g'(x)	2
9845173145	d/dx sin x	cos x	3
9845173875	d/dx cos x	-sin x	4
9845174721	d/dx tan x	sec^2(x)	5
9845176340	d/dx cot x	-csc^2(x)	6
9845179908	d/dx sec x	sec x tan x	7
9845181052	d/dx csc x	-csc x cot x	8
9845183167	d/dx e^x	e^x	9
9845184498	d/dx ln x	1/x	10
9845190618	L'Hopital's Rule		11
9845192678	Continuity	Limit from the left = Limit from the right = Function value	12
9845205842	Critical Numbers	Occur where f'(x) = 0 or f'(x) DNE (denominator = 0)	13
9845212914	POSSIBLE Points of Inflection	Occur where f''(x) = 0 or f''(x) DNE (denominator = 0)	14
9845213959	Points of Inflection	Occur where f''(x) has a sign change	15
9845219022	Extreme Value Theorem	Absolute/Global extrema on a closed interval must occur either at a critical number or at endpoints	16
9845225127	Relative/Local Maximum (First Derivative Test)	Occurs where f' changes from positive to negative	17
9845227660	Relative/Local Minimum (First Derivative Test)	Occurs where f' changes from negative to positive	18
9845232720	Relative/Local Maximum (Second Derivative Test)	Occurs when f''(critical number) < 0	19
9845241819	Relative/Local Minimum (Second Derivative Test)	Occurs when f''(critical number) > 0	20
9845245263	Local Linear Approximation	y - y1 = m ( x - x1) (Equation of a Tangent Line)	21
9845249171	Fundamental Theorem of Calculus		22
9845254381	Second Fundamental Theorem of Calculus		23
9845263310	Mean Value Theorem		24
9845269381	Average Value of a Function		25
9845272308	Intermediate Value Theorem		26