netwons method doing that jawn i am a bo$$ students will be able to use newton’s method to find...

NETWONS METHOD

DOING THAT JAWN

I AM A BO$$

STUDENTS WILL BE ABLE TO USE NEWTON’S METHOD TO FIND THE ROOTS OF ALGEBRAIC EXPRESSIONS

TEACH ME HOW TO NEWTON’S METHOD!!!

USES

• Approximating the Zeros of a function

• Finding Intellectual Enlightenment

• Having Fun

Basic Formula

)('

)(

0

001 xf

xfxx

How to Do It

1) Read the Problem2) Make a guess of the root3) Calculate Initial Approximation using this

guess4) Continue until is close to 0|| 1 nn xx

Visual Representation

1) Find where the line tangent to the first guess intersects the x axis2) Make this the new guess3) Keep on repeating that jawnslice

Practical Application

1)( xxfI’m an expert at Math, so I guess that x=2

)2('

)2(2

f

f

Which means…

= 11

32

So we do this again with a guess of -1

)1('

)1(1

f

f= 1

1

01

|| 1 nn xx = 0 So we know this is a root

•Now let’s get a little harder!

FIND THE SQUARE ROOT OF 2

2)( 2 xxfGuess that x= 1.5

)5.1('

)5.1(5.1

f

f 417.1

3

25.5.1 =

Guess that x= 1.417

)417.1('

)417.1(417.1

f

f 414.1

834.2

007.417.1 =

THIS IS VERY CLOSE TO THE KNOWN ROOT OF 1.4142

NOW FOR THE FUN STUFF

Harder Stuff

1)( 25 xxxf

Guess that x=.8

)8(.'

)8(.8.

f

f = 785.

648.3

03232.8.0

Make .785 your new guess and repeat

)785(.'

)785(.785.

f

f 809.

4733.3

0856.785.0

=

Since the answer only changed by .024, this is very close to a root

HAVE FUN DOING THE CALCULUS