The curve C C\,C has the equation y=(10−x)lnxy = (10 - x) \ln xy=(10−x)lnx, x>0x > 0x>0.
Find dydx\displaystyle \frac{dy}{dx}dxdy
C C\,C has a stationary point at PPP. Show that the xxx-coordinate of P P\,P lies between 4 and 4.5.
Show that the xxx-coordinate of P P\,P is a solution of x=101+lnx\displaystyle x = \frac{10}{1 + \ln x}x=1+lnx10.
Use the iteration formula xn+1=101+lnxn\displaystyle x_{n+1} = \frac{10}{1 + \ln x_n}xn+1=1+lnxn10 with x0=4.25x_0 = 4.25x0=4.25 to find, to 3 decimal places, the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3.
Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only), matched to the AQA A Level Maths (7357) 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.
