Matter and Motion

Fall 2004

Review chart for Calculus—week 4

 

general topic

recognition / standard form / notation

reference example

basic operations

Library of Functions

 

 

• evaluate on calculator

• graph on calculator

• find specific member of family for specific situation

            linear

mx+b

temperature conversion

 

            exponential

10x, ex

population growth

 

            logarithmic

log x, ln x

inverse of exponential

 

            trigonometric

sin x, cos x, tan x

height of tide

 

            stretches and shifts

f(x-a), kf(x)

y=k(x-a)2

 

            inverse

 

logarithim

 

 

 

 

 

The Derivative Concept

 

 

 

            derivative at a point

f’(a), dy/dx|x=a

speed at an instant

estimate for given function and point,

calculate exactly using limits

            derivative function

f’(x), dy/dx

 

calculate exactly using limits

 

 

A possible essay question:

 

For a given pair of the following concepts, give a definition of each, and write a short paragraph explaining the connection between them and any important distinctions between them.

the derivative at a point / the derivative function / slope of a curve at a point / difference quotient / limit

 

Example: function / domain / range

 

A function is a rule that takes certain numbers as inputs and assigns to each a definite output number.

The domain of a function is the set of all input numbers allowed for that function.

The range is the set of all output numbers which that function can generate.

 

Domain/Range: the domain of a function and the range of a function are connected by the fact that each number in the domain is connected to some number in the range. The most important distinction between them is that domain refers to inputs and range to outputs.