Math 115

Notes

Class

meetrng

t

to

Preliminary

Notes

*What

kind

of

problem

necessitates

the

calculation of

a derivative:

-Look

for the following

words &

phrases:

'ollow

fast

is a

quantrty

changing

at a

given

value"

"Find the rate

of change

of a

quantity

wrt to another

quantlty

at a

given

value"

o'Find

the velocity of

a

particle

at a

given

time value"

(for

distance-time

functions)

-All

functions

are categorized

into two

groups

(1)

Algehraic

-We

have been

dealing

with

group

1 so far

-Group

1 functions

are composed

totally by algebraic operations

of :

Addition, subtraction,

multiplication, division, numerical

powers

or roots.

Example:

(x):13x'

- 5x1t2Y{7

+t

(all

operations involved

are

algebraic)

Polynomial functions

(polys

for

short) are

a

subclass thatar:e

simple looking & behave nicely---

differentiable

for all

x in its domain

Example:

y:l4x' -23x4 -26x+19

(smooth

everywhere)(which

makes them continuous everywhere)

(2)

Non-algebraic)--called

"Transcendental"

-Composed

with a least one operationthat

is non-algebraic

Examples: Exponential:

y:2',

Logarithmic:

(x):

log z

(x'+1),

Trigonometric:

y:3sin3x+5cos7x

-These

may be

very

complex

looking. Most

growth/decay

models

& engineering applications

use

these

types of functions....there

are

others

in advanced

courses

not mentioned

here...

-Also,

advance

problems

in

business applications

(mostly

economics related) use these fypes of

models....you will see some on

the

practice

problems

&

the exffa credit...