The curve C C\,C has the equation y=(12−x)lnxx>0y = (12 - x) \ln x \quad x > 0y=(12−x)lnxx>0
Verify that dydx=−lnx+1x(12−x)\displaystyle \frac{dy}{dx} = -\ln x + \frac{1}{x}(12 - x)dxdy=−lnx+x1(12−x)
C C\,C has a stationary point at PPP. Show that the x x\,x coordinate of P P\,P lies between 4.5 and 5
Show that the x x\,x coordinate of P P\,P is a solution of x=121+lnx\displaystyle x = \frac{12}{1 + \ln x}x=1+lnx12
Use the iteration formula xn+1=121+lnxn\displaystyle x_{n+1} = \frac{12}{1 + \ln x_n}xn+1=1+lnxn12 with x0=4.75x_0 = 4.75x0=4.75 to find, to 3 decimal places, the values of x1,x2 x_1, x_2\,x1,x2 and x3x_3x3.
329 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.