other random stuff

mean value theorem

f’(c ) = f(b)-f(a)/b-a

rolle’s theorem

f’(c ) = 0

trapezoid formula

h/2(b1+b2)

fundamental theorem of calculus

a-bf(x)dx=F(b)-F(a)

corollary to funthmcalculus

f(b(x))b’(x) - f(a(x))a’(x)

critical point

f’=o or DNE

trap rule

h/2(b1+b2)

average velocity

s(b)-s(a)/b-a

average acceleration

v(b)-v(a)/b-a

intermediate value theorem

if a function is continuous on [a,b] and k is a number between f(a) and f(b) then there exist c in (a,b) such f(c )=k

vertical asymptote

x=b and x goes to infinity

horizontal aymptote

y=1 and n/m cases

differentiability

no cusps, corner, vertical tangents, discontinuity

integration

area

differentiation

slope

continuous at a point

limx-a^-=limx-a^+=limx-a=f(a)

reciprocal secx

1/cosx

reciprocal cscx

1/sinx

-sinx

odd

cosx

even

ftc 2 (easy)

f(x)

another ftc

f(b)-f(a)

seperation of variables

y=ce^kt

optimization

1 write function in one variable, 2 find first deriv = 0, 3 check endpoints