The curve with equation y=f(x)y = f(x)y=f(x) has a turning point at PPP. The xxx-coordinate of P P\,P is α\alphaα.
Show that α=16e−α\displaystyle \alpha = \frac{1}{6} e^{-\alpha}α=61e−α.
The iterative formula xn+1=16e−xn,x0=1,\displaystyle x_{n+1} = \frac{1}{6} e^{-x_n}, x_0 = 1,xn+1=61e−xn,x0=1, is used to find an approximate value for α\alphaα. Calculate the values of x1,x2,x3 x_1, x_2, x_3\,x1,x2,x3 and x4x_4x4, giving your answers to 4 decimal places.
By considering the change of sign of f′(x)f'(x)f′(x) in a suitable interval, prove that α=0.1443\alpha = 0.1443α=0.1443 correct to 4 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.