A structural beam's vertical deflection D(x)D(x)D(x) (in mm) at a distance xxx (in metres) from the left support is modeled by the function
D(x)=x4−6x3+5x+12,x≥0D(x) = x^4 - 6x^3 + 5x + 12, \quad x \ge 0D(x)=x4−6x3+5x+12,x≥0
Show that the equation D(x)=0D(x) = 0D(x)=0 has a root, α\alphaα, in the interval [5.5,6.0][5.5, 6.0][5.5,6.0].
Show that the equation D(x)=0D(x) = 0D(x)=0 can be rewritten in the form
x=6x2−5−12x3x = \sqrt[3]{6x^2 - 5 - \frac{12}{x}}x=36x2−5−x12
The iterative formula
xn+1=6xn2−5−12xn3x_{n+1} = \sqrt[3]{6x_n^2 - 5 - \frac{12}{x_n}}xn+1=36xn2−5−xn12
is used to find α\alphaα.
Starting with x1=5.7x_1 = 5.7x1=5.7 and using the iterative formula,
(i) find, to 4 decimal places, the value of x2x_2x2.
(ii) find, to 4 decimal places, the value of α\alphaα.
Practise Edexcel A Level Maths 10.2 Iteration with exam-style questions for A Level Maths. 32 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 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.