TERM 1
Mean Value Theorem
DEFINITION 1
Suppose y = f(x) is continuous on the closed interval [a; b]
and dierentiableon the open interval (a; b) . Then there
exists a c in (a; b) such thatf '(c) =f(b)-f(a)/b -a
TERM 2
Properties of Natural Logarithms
DEFINITION 2
ln(ab)= ln(a) + ln(b)ln(a/b)= ln(a)- ln(b)ln(a^b)=
bln(a)ln(1)=0e^ln(a)= a
TERM 3
Logarithmic Differentiation
DEFINITION 3
Steps:1. take ln of both sides of the equation2. use log rules
to simplify3. use implicit differentiation to find dy/dx4.
makesubstitutionsso that y is in terms of x
TERM 4
Point of Inflection
DEFINITION 4
set second derivative equal to zero or undefined. then test
the values for changes in concavity (changes in positive or
negative)
TERM 5
Absolute Max and Min
DEFINITION 5
set first deravitive equal to zero or undefined, this will give
you critical points. To find min and max, test critical points
and endpoints by plugging them into the original equation
and finding the greatest and lowest y value
