Question

Use MatLab.

Using f(x) = x^5 - 9x^4 - x^3 + 17x^2 - 8x -8 and x0 = 0, study and explain the behavior of Newton's method.

Hint: The iterates are initially cyclic

Answer 1

steps to find root using newrons method:-

1)check if the function is differentiable or not.if and only if function is differentiable then only it can be applied.

2)find first derivative f’(x) of given function

3)put initial guess of root of eqn.

4)use newtons iteration formula as:x2 = x1 – f(x1)/f’(x1)
        repea the process for x3,x4..till tha actual root is found out.

inp=input("enter the function in variable x:","s");

x(1)=input("enter initial guess");

error=input("enter allowed error");

fun=inline(inp)

dif=diff(sym(inp));

val=inline(dif);

for i=i:100

x(i+1)=x(i)-((f(x(i))/d(x(i))));

err(i)=abs((x(i+1)_x(i))/x(i));

if err(i) < error

break

end

end

root=x(i)