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anonymous
 5 years ago
use newton's method to estimate the requested solution of the equation. start with given value of Xo and then give X2 as the estimated solution. 3x^2+2x1=0; Xo = 1; Find the righthand solution.
anonymous
 5 years ago
use newton's method to estimate the requested solution of the equation. start with given value of Xo and then give X2 as the estimated solution. 3x^2+2x1=0; Xo = 1; Find the righthand solution.

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0get the derivative, so you know the slope of the line at x0 = 1

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0find the value of f(1) so you have a set of coordinates to use for your "equation of the slope" line to find the new "x1" with.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(1) = 4; (1,4) we will use this to calibrate our line equation with; now we find the slope at f(1)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f'(x) = 6x +2 f'(1) = 8 ; our slope is 8 y = mx+b 4 = 8(1) + b 4 = 8 + (4) y = 8x 4 find the root :) the x int and that your "new" X value

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when y = 0 we have our x intercept, (x,0) is the x int..

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.00 = 8x 4 x = 4/8 = 1/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right. man your awesome

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0to keep punching along, we use the NEW x value in our original equation and keep getting closer and closer to our "true" root ;) or farther away depending on the nature of the curve

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i see. hey is there a way to find the critical points of a function on a calculator instead of using calculus

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0calculus is the "method" of the math used to find this stuff. calculus is applied to the situation when nothing else can get us there :) So I would say that it depends on the calculator and the functions that it has. But in the end, they rely upon the principles of calculus to get the answer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0true. well maybe since ur smart you can help with a calc problem i have.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the other maths are really applied calculus :) tell me, is the earth round or flat?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i might be able to help....my smarts come and go lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0calculus, in essense, says that in order to figure out a problem you ahve to get close enough to it to "flatten" things out to where we can use our innate understanding of the "flat" world around us :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Interesting we'll hv to chat more abt that... i'm trying to Find the function with the given derivative whose graph passes through the point P. r'(t) = sec^2t  4, P(0,0)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0that would be an integral. or antiderivative.. same thing different jargon. [S] sec^2(t)  4 dt or \[\int\limits_{}\sec^{2}  4 dt\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0just like dressing down into the derivative, we just suit up into the integral... they are opposite movements

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0[S] sec^2(t) dt 4 [S] dt does this make sense?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol not really. the answer i came up with is sec t  4t  4

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0what function do you know that dress down to a derivative of sec^2? what function do you know that dress down to a derivative of 1 ?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lets check that:....or it looks like you already did

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x dresses down to 1 d(1x) = 1 that is correct. So what do we dress "1" to be? x right? we just back out of the derivative into the original function right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.04 [S] dt > 4t now for the left part :) sec^2 came from what? do you recall your trig dervivatives?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I think: d(tan(x)) = sec^2 did I recall correctly?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so would the answer be tan t  4t

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I think im right to, but Ive been known to be mistaken ;) so: [S] sec^2(t) dt suits back up into tan(t) our original equation is of the form: f(x) = tan(t) 4t but that aint it exactly...that just gives us a "family" of curves to choose from...we need to pin this down with a constant

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0tell me, can 2 different equations have the exact same derivative? y = 2x^2 + 6 y = 2x^2 8

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0that right: so what we have right now is an equation to a curve that is actually floating up and downthe y axis and we need to pin it down with something....... we do that with a constant (C). like this: y = tan(t) 4t +C

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0does that make sense?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0that is getting to our answer, remember they gave us an initial condition that the curve passes thru the point (0,0) right? so lets use this information to find the actaul value for "C".

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0P(0,0) 0 = tan(0) 4(0) + C solve for C :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0thats right, but now we "know" for sure :) so the equation is: r = tan(t) 4t and were done :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i like how you make sure i know where the answer is coming from. you would make a great instructor

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0thanx; I figure that if I show you whats going on under the problem that you might just be able to use it in another place ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i'm working on this word problem. "From a thin piece of cardboard 40in. by 40in., square corners are cut oout so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? what is the maximum volume rounded to nearest tenth if necessary

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Volume is to maximized so we need the formula for the volume of a box: Do you know what that would be?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0length x width x height, right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0thats correct; when we cut out these corners and fold them up, that is our "height" right? lets call that x..ok?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0length and width are equal measurements given the problem, 40 and 40 right? when we remove "x" from on end and "x" from the other; that makes our sides shorter by x+x. length then becomes: 40 2x and width becomes: 402x lets use this in our formula for volume: V = (402x)(402x)(x) we agree?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we can factor out x right

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0factor out? now, we need to multiply all these together to find the equation for derive :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0so far our box is like this:

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0V = (402x)(402x)(x) V = 1600x 160x^2 +4x^3 you wanna derive this for me?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sure i got 1600  320x + 12x^2

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0thats right... now we need to equal that to 0 to find our max and min.... for x :) 4(3x^2 80x +400) = 0 3x^2 80x +400 = 0

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0this gives me 2 numbers: x = 40/3 and x = 20/3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0both of these numbers should give us an equal volume of box, but different shapes.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0unless I am mistaken, and I think I am with that last one...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0plug both of these into our forula stuff and see which is bigger :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0V = (402(40/3)) (402(40/3)) (40/2) V = (402(20/3)) (402(20/3)) (20/3) we only have one formula for volume that needs a value for x ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.020/3 yields a bigger answer

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0for 40/3 we get 2014.81 .....then 20/3 it is :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep, for 20/3 we get 7407.41

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, I noticed that I punched in the wrong thing in the calculator :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the bigger # is the volume?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep....when we cut out a corner of "20/3" from each side, we have gotten the maximum volume we can get out of it
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