i need help please

[charred widget]

How can i solve this h.w please

[mellow latch]

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[next grove]

@wise crag

[wise crag]

@next grove

NO I WAS GONNA DO THAT

[mossy salmon]

@mossy salmon

[wise crag]

I have zero clue how to solve this

Newton Raphson?

[wise crag]

Ok are you supposed to prove it?

[charred widget]

Yes

[wise crag]

The photo is already giving you a clue

[charred widget]

Yes

[wise crag]

Get the tangent line to a point

And itterate

[charred widget]

What point can i use

[wise crag]

Uhm in the Newton Raphson method you start with a random one

For your proof you have to use a random one too I guess

[charred widget]

Can i use [1,0]

[wise crag]

Well they're asking you to prove it, aren't they?

[charred widget]

Yes

[wise crag]

So you have to use a generic one

[charred widget]

But without using taylor series

[next grove]

use x_n

[wise crag]

Like $x_0$

[frail bolt]

ϕ Miguel

[next grove]

Use x_n

for more generality

[wise crag]

No, x_0 for the first itteration

x_n for the n+1th itteration

[next grove]

okay sure

lets use x_0

what is the eqn of tangent of f(x) at x_0

[wise crag]

So now write the tangent line to the function at x_0

[next grove]

@charred widget

[wise crag]

Omg Wolf why you type so fast

[next grove]

im typing slow rn lmao

[charred widget]

Lol

[wise crag]

Smh

[charred widget]

I love u guys

[next grove]

love you too

[charred widget]

Awww

So now

Do i have to write down the rule

Of newton

[wise crag]

No, you have to find the rule

And for that you need to know the tangent line to the function at x_0

[next grove]

yeah first find that

[wise crag]

Oh I see why Wolf wanted x_n

Yeah do it for x_n

[charred widget]

Im thinking wait

Y-y1=m(x-x1)

So instead of y what should i use

[wise crag]

And how does y relate to the derivative of y?

[wise crag]

You can write f(x)

So

$f(x)-f(x_n)=m(x-x_n)$

[frail bolt]

ϕ Miguel

[next grove]

man

[wise crag]

Now you need to know how m relates to the derivative of f

So everything is in terms of f and x_n

[next grove]

i think

they have been taught the equation of the tangent

@charred widget have you not

if not then miguel continue

[wise crag]

They've written it

[charred widget]

Even if i learnet i forgot

The formula u mean

[wise crag]

So do you know that the derivative at some point is the slope of the tangent line to the function at that point?

[charred widget]

Ugh

No

Wiat

Yes

[wise crag]

Ok great

So instead of m

We can write

[charred widget]

This right

[wise crag]

Yyeer

$f'(x_n)$

[frail bolt]

ϕ Miguel

[wise crag]

We can write that instead of m

[charred widget]

Why

[charred widget]

Because of this right

[wise crag]

Because $m=f'(x)$

Yes

[frail bolt]

ϕ Miguel

[wise crag]

At every point

For example

f(x) = x²

f'(x) = 2x

f'(2) = 4

So we know that the tangent line to the function at x = 2 has a slope of 4

You can check it visually

,w graph x^2, 4x-4

[charred widget]

WOW

[frail bolt]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by mig.uel

[wise crag]

There it is

[charred widget]

They have the same point

[wise crag]

Yee

So let's write out equation

$f(x)-f(x_n)=f'(x_n)(x-x_n)$

[frail bolt]

ϕ Miguel

[wise crag]

Everything in terms of x_n and f, great

[wise crag]

So now we need to know where the tangent line is equal to 0

As your gif shows

Because that will be the next x

[charred widget]

But why zero

[wise crag]

Do you see that the new point is where the tangent crosses the x axis?

[charred widget]

Because it get closer to zero

Right

[wise crag]

Yes, the slope is always smaller and smaller

[charred widget]

I feel smart

[wise crag]

Nice

So we're looking when f(x) = 0

Right?

[charred widget]

U

Um

[wise crag]

Not the original function

Our tangent function

[wise crag]

This one

[charred widget]

So we substitute zero in f(x)

[wise crag]

Maybe using f for both the original function and the tangent function is a bad idea

[wise crag]

Anyway we set f(x) = 0 yes

$f(x)=f'(x_n)(x-x_n)+f(x_n)=0$

[frail bolt]

ϕ Miguel

[wise crag]

And now you just have to isolate x there

[charred widget]

I get it

[wise crag]

And you'll get the Newton formula

[charred widget]

We divide it by (x-x_n)

Right

No

[wise crag]

$f'(x_n)(x-x_n)+f(x_n)=0$

[frail bolt]

ϕ Miguel

[wise crag]

First of all we take the f(x_n) thing to the other side

[charred widget]

We get this

[wise crag]

$f'(x_n)(x-x_n)=-f(x_n)$

[charred widget]

Yes

[frail bolt]

ϕ Miguel

[wise crag]

And now you divide by f'(x_n)

[charred widget]

Yes

[wise crag]

$(x-x_n)=\frac{-f(x_n)}{f'(x_n)}$

[frail bolt]

ϕ Miguel

[wise crag]

And you finally move x_n to the other side

[wise crag]

$x=x_n-\frac{f(x_n)}{f'(x_n)}$

[frail bolt]

ϕ Miguel

[wise crag]

And as we are gonna use that x as our new x_n

We call it x_n+1

$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$

[frail bolt]

ϕ Miguel

[charred widget]

Miguel i love u so much THANK U SO MUCH U SAVED MY LIFE

[wise crag]

Which is the Newton Raphson Formula

[wise crag]

No problem!!

[charred widget]

THANK U SO MUCH I REALLY APPRICIATE UR TIME

♥️💖💓💝💞💝💓💘💓💘