f(x)=3x3−2x−6f(x) = 3x^3 - 2x - 6f(x)=3x3−2x−6.
Show that f(x)=0f(x) = 0f(x)=0 has a root, α\alphaα, between x=1.4x = 1.4x=1.4 and x=1.45x = 1.45x=1.45.
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written as
x=(2x+23),x≠0. x = \sqrt{\left(\frac{2}{x} + \frac{2}{3}\right)}, \quad x \neq 0. x=(x2+32),x=0.Starting with x0=1.43x_0 = 1.43x0=1.43, use the iteration
xn+1=(2xn+23) x_{n+1} = \sqrt{\left(\frac{2}{x_n} + \frac{2}{3}\right)} xn+1=(xn2+32)to calculate the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3, giving your answers to 4 decimal places.
By choosing a suitable interval, show that α=1.435\alpha = 1.435α=1.435 is correct to 3 decimal places.
Practise Edexcel A Level Old Maths Numerical Methods with exam-style questions for A Level Old Maths. 7 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.