The curve C has the equation y=(12−x)lnxy = (12 - x) \ln xy=(12−x)lnx, x>0x > 0x>0
Find dydx\displaystyle \frac{dy}{dx}dxdy
C has a stationary point at P. Show that the x x\,x coordinate of P lies between 4.5 and 5
Show that the x x\,x coordinate of 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 x1x_1x1, x2 x_2\,x2 and x3x_3x3.
