AP Calc Flashcards

9909550027	Velocity	Derivative of position	0
9909550028	Acceleration	Derivative of velocity	1
9909550029	Speed	Absolute value of velocity	2
9909550030	Displacement	How far the particle is from where it started (y2-y1).	3
9909550031	Position	Where the particle is at a given time.	4
9909550032	Average velocity given a position function	(y2-y1) / (x2-x1)	5
9909550033	Particle is moving right	Velocity is positive	6
9909550034	Particle is moving left	Velocity is negative	7
9909550035	Acceleration is positive	Velocity is increasing (slope of vel. graph is pos.)	8
9909550036	Acceleration is negative	Velocity is decreasing (slope of vel. graph is neg.)	9
9909550037	Particle changes direction	Velocity changes signs	10
9909550038	Maximum height of an object	Set velocity equal to zero and check for a sign change.	11
9909550039	Particle at rest	Velocity equals zero.	12
9909550040	Increasing speed	Velocity and acceleration are the same sign.	13
9909550041	Decreasing speed	Velocity and acceleration are opposite signs.	14
9909550042	Derivative of sin x	cos x	15
9909550043	Derivative of cos x	-sin x	16
9909550044	Derivative of tan x	sec^2(x)	17
9909550045	Derivative of cot x	-csc^2(x)	18
9909550046	Derivative of sec x	sec x tan x	19
9909550047	Derivative of csc x	-csc x cot x	20
9909550048	Product rule	first times derivative of 2nd plus 2nd times derivative of first.	21
9909550049	Quotient rule	low d high minus high d low all over low squared.	22
9909550050	Power Rule for x^n	nx^(n-1)	23
9909550051	Derivative of a constant	0	24
9909550052	Equation of a line	(y-y1)=m(x-x1)	25
9909550053	Equation of a normal line	(y-y1)=-(1/m)(x-x1)	26
9909550054	Horizontal tangents	Set derivative equal to zero.	27
9909550055	Not differentiable if...	Corners, cusps, vertical tangents, discontinuities	28
9909550056	4 types of discontinuity	Jump, removable, infinite (asymptote), oscillating	29
9909550057	Continuous but not differentiable	Corners, cusps, vertical tangents	30
9909550058	Definition of continuity at a point	function value = limit value	31
9909550059	Differentiability from a piecewise	Check continuity (functions have the same y) and differentiability (same derivatives).	32
9909550060	Sketching the derivative	Find the zero slopes and then pay attention to pos. or neg. slope.	33
9909550061	How we treat the nth root of x	x^(1/n)	34
9909550062	How we treat 1/x^n	x^(-n)	35
9909550063	Slope from a point on a table	Find the slope of the point above and below.	36
9909550064	Increasing	f' is positive	37
9909550065	Decreasing	f' is negative	38
9909550066	Concave up	f'' is positive	39
9909550067	Concave down	f'' is negative	40
9909550068	Inflection point	f" changes sign or f' goes from inc. to dec. (or vice versa)	41
9909550069	Critical point	f'=0 or f' is undefined	42
9909550070	Where to look for max and mins	Critical points and endpoints	43
9909550071	Mean Value Theorem	Closed, continuous, and differentiable - there is a point c where avg slope = inst. Slope	44
9909550072	Extreme Value Theorem	Closed and continuous - There will be an absolute max and min	45
9909550073	Intermediate Value Theorem	Closed and Continuous - Every y value gets hit on the way from f(a) to f(b)	46
9909550074	L'Hopital	If indeterminate - derive the top and bottom.	47
9909550075	Area of a trapezoid	½ the height times the sum of the 2 bases	48
9909550076	Growth formula for dy/dx = ky	y=Ae^(kt)	49
9909550077	How to find vertical asymptotes	set denominator = 0	50
9909550078	How to find horizontal asymptotes	find the lim as x approaches positive and negative infinity	51
9909550080	Change in position (displacement)	integrate v(t)dt from a to b	52
9909550081	Total distance traveled		53
9909550082	Average value of a function		54