Question

using matlab

3. [1:2] Find a root (value of x for which f(x)-0) of f(x) = a x^3 + bx^2 + c x + d using Newton's interation: xnew = x -f(x)/(x). Note that f'(x) is the first derivative off with respect to x. Then x=xnew. Start with x=0 and iterate until f(xnew) < 1.0-4. Use values (a,b,c,d]=[-0.02, 0.09, -1.1, 3.2). Plot the polynomial vs x in the range (-10 10). Mark the zero point.

Answer 1

`Hey,

Note: If you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc%clears screen
clear all%clears history
close all%closes all files
a=-0.02;
b=0.09;
c=-1.1;
d=3.2;
f=@(x) a*x.^3+b*x.^2+c*x+d;
g=@(x) 3*a*x.^2+2*b*x+c;
hold on;
fplot(f,[-10,10]);
x0=0;
for i=1:100
x0=x0-f(x0)/g(x0);
if(abs(f(x0))<1e-4)
break;
end
end
disp(x0);
plot(x0,f(x0),'*r');

- O X Pradeep EDITOR PUBLISH VIEW do E C . Search Documentation 3 Insert & fx F Comment % 92% Indent & - O X Breakpoints Run - Run and Advance Run Spatina > Advan Jual Figure 1 File Edit & View Insert EDIT BREAKPOINTS RUN Tools Desktop Window ORA Help O E O A MATLAB R2018 HOME PLOTS APPS L A Find Files 2 3 Compare - Go To - New Open Save Print Find FILE NAVIGATE hal Windows System32 Current Folder Name 0409 1029 1033 1036 1040 1045 1046 1049 1055 3082 Advancedinstallers af-ZA am-et AppLocker appraiser Details 7 Editor - C:\Users\PRADEEP KALRA\Documents\MATLABY 1+1 saveee. m x bisectionmethodbypradeep. m y g=@ (x) 3*a*x.^2+2*b*x+c; hold on; fplot (f,(-10,10]); x0=0; for i=1:100 x0=x0-f(x0)/g(x0); if (abs (f(x0) ) <le-4) break; end IIIIIIIII Command Window 3.1526 fx >> Workspace Name Value -10 -8 6 4 -2 0 2 4 6 8 10 b -0.0200 0.0900 - 1.1000 3.2000 @(x)a*x.^3+b*x.^2+... @(x)3*a*x.^2+2*b*x+c d xo 3.1526 script In 10 Col 9 ENG 11:53 PM IN 02/28/20 Type here to search

Kindly revert for any queries

Thanks.