AP Calculus General Stuff Flashcards

Stuff I should know

5824941450	Log A + Log B	Log (AB)	0
5824941451	Log A - Log B	Log (A/B)	1
5824941452	k Log A	Log (A^k)	2
5824941453	Point-slope form of a line	y-y1 = m (x-x1)	3
5824941454	Product rule	d/dx (uv) = uv' + vu'	4
5824941455	Quotient rule	d/dx (u/v) = (vu'-uv')/(v^2)	5
5824941456	Rolle's Theorem	Let f be continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 somewhere in the interval).	6
5824941457	Mean Value Theorem	If f is continuous on [a,b] and differentiable on (a,b), then there exists a number c on (a,b) such that f'(c)=(f(b)-f(a))/(b-a)	7
5867821787	Approximating binomial powers (1+f)^k	(1+f)^k ≈ 1+kf where f is some function	8
6039920360	Maximum profit	Marginal revenue (r') = Marginal cost (c')	9
6039922015	Minimize average cost	Average cost = marginal cost c(x)/x=c'(x)	10
6039931314	Linearization	L(x) = f'(a)(x - a) + f(a)	11
6039936205	Definition of differentials	dy = f'(x) dx	12
6039939750	Absolute change, true	Δf = f(a + Δx) - f(a)	13
6039999167	Absolute change, estimated	Δf ≈ f'(a) Δx	14
6040004272	Relative change, true	Δf/f(a)	15
6040007065	Relative change, estimated	f'(a)/f(a) Δx	16
6040009721	Percentage change, true	Δf/f(a) X100	17
6040011750	Percentage change, estimated	f'(a)/f(a) Δx X100	18
6040021754	Newtons Method for approximating zeroes	Coming soon	19