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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
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TEACH ME HOW TO NEWTON’S METHOD!!!
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USES
• Approximating the Zeros of a function
• Finding Intellectual Enlightenment
• Having Fun
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Basic Formula
)('
)(
0
001 xf
xfxx
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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
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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
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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
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•Now let’s get a little harder!
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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
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NOW FOR THE FUN STUFF
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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
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HAVE FUN DOING THE CALCULUS