The function f f\,f is defined by f(x)=exx−1f(x) = e^x \sqrt{x} - 1f(x)=exx−1
f(x)=0f(x) = 0f(x)=0 has a single solution at the point x=αx = \alphax=α. By considering a suitable change of sign, show that α \alpha\,α lies between 0 and 1
Show that f′(x)=ex(2x+1)2x\displaystyle f'(x) = \frac{e^x(2x + 1)}{2\sqrt{x}}f′(x)=2xex(2x+1)
Use the Newton-Raphson method with x1=1x_1 = 1x1=1 to find x3x_3x3, an approximation for α\alphaα. Give your answer to five decimal places
Explain why the Newton-Raphson method fails to find α \alpha\,α with x1=0x_1 = 0x1=0
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.