Quadratic Formula

a x2+bx+c=0

x=−b±√b2−4ac2a

Factoring Polynomials

x2− y2=( x+ y ) ( x− y )

x3+ y3=( x+ y ) (x2−xy+ y2 )

x3− y3= (x− y ) (x2+xy+ y2 )

Natural logs and exponents

f ( x )=ln ( x )

x=e f (x)

f ( x )=ex

x=ln ( f ( x ))

Cealn (b )=Cba

Cea+ln (b )=Cbea

Cea−ln (b)=C ea

b

Ce ln (b)−a=Cbe−a

ln (a∗b )=ln (a )+ln (b )

ln (a /b )=ln (a )−ln (b )

Geometry

Triangle :

A=12bh=1

2ab sin θ

:̊

A=π r2

C=2πr

Product Rule

h ( x )=f (x ) g ( x )

h' ( x )=g ( x ) f ' ( x )+f ( x )g ' ( x )

Quotient Rule

h ( x )= f ( x )g (x )

h' ( x )=g ( x ) f ' ( x )−f ( x )g ' ( x )

[ g ( x ) ]2

Lagrange Multipliers

Given f ( x , y ) s . t . g (x , y )=0 ,

L ( x , y , λ )=f ( x , y )+λg ( x , y )

Set∂L∂ x

=0 , ∂ L∂ y

=0 , ∂ L∂ λ

=0

OR

Given f ( x , y ) s . t . g (x , y )=k ,

f x ( x , y )=λ gx (x , y )

f y ( x , y )=λ g y ( x , y )

g ( x , y )=k