Differentiation of Exponential and Logarithmic
Functions
Exponentialfunctionsandtheircorrespondinginversefunctions,calledlogarithmic
functions,havethefollowingdifferentiationformulas:
Notethattheexponentialfunctionf(x)=exhasthespecialpropertythatitsderiva
Tangent Lines
The first problem that were going to take a look at is the tangent line problem.
Before getting into this problem it would probably be best to define a tangent
line.
A tangent line to the function f(x) at the point
is a line that
just touche
Rates of Change
Here we are going to consider a function, f(x), that represents some quantity
that varies as x varies. For instance, maybe f(x) represents the amount of water
in a holding tank after x minutes. Or maybe f(x) is the distance traveled by a c
Velocity Problem
Velocity is nothing more than the rate at which the position is changing.
In other words, to estimate the instantaneous velocity we would first compute
the average velocity,
Change of Notation
Notice that whether we wanted the tangent lin