Question

plot the graph of y=3x^3 - 2x^2 +x - 10 for the values of x from -10 to 10 using matlab command and apply Newton Raphson method to find the positive root of the equation y=3x^3 - 2x^2 +x - 10 using matlab

Answer 1

then i guess you need matlab!

Answer 2

for plotting
x = -10:0.1:10;
plot(x, 3x^3 - 2x^2 +x - 10)

Answer 3

can you explain is short sentence how newtonw raphson method works??

Answer 4

no

Answer 5

its like lagrangian interpolation

Answer 6

I wouldn't say that

Answer 7

looks like this is getting interesting

Answer 8

Is there a newtions method command in matlab?...or are you supposed to program one?

Answer 9

i dont need the matlab help, i need manual help...using newton raphson method

Answer 10

I assume you know the iterative formula?

Answer 11

For Newton Raphson Method

First find f(x)
then using the equation
x_n+1 = x_n - f(x_n) / f'(x_n)
find the required formulae

Answer 12

yes

Answer 13

do you have your initial guess \(x_0\)?

Answer 14

no i havent attempted yet

Answer 15

ok...where exactly are you stuck?

Answer 16

so how do we use it to find the roots?

Answer 17

pick a number you think will be close to a solution to
\[3x^3 - 2x^2 +x - 10=0\]

Answer 18

that is your first guess, say
\[x_0\]
second guess will be
\[x_0-\frac{f(x_0)}{f'(x_0)}\]

Answer 19

i guess i understand it not ... hahahah

Answer 20

*now

Answer 21

if you pick
\[x_0=\frac{5}{3}\] you are done in one step since
\[f(\frac{5}{3})=0\]

Answer 22

if you pick say
\[x_0=2\] then your second guess will be
\[2-\frac{f(2)}{f'(2)}\]

Answer 23

\[f(2)=8\]
\[f'(x)=6x^2-4x+1\]
\[f'(2)=17\]
\[2-\frac{8}{17}=\frac{26}{17}\] is your second guess

Answer 24

is there some kind of error here
function xn = function_newt(x)
xn = x - (3*x^3 - 2*x^2 +x - 10)/(9*x^2 - 4*x +1);

Answer 25

satellite73 just has a small typo in his derivative.

Answer 26

x = 3;
for i = 0:10
x = function_newt(x);
end
disp(x)

Answer 27

function xn = function_newt(x)
xn = x - (3*x^3 - 2*x^2 +x - 10)/(9*x^2 - 4*x +1);