f(x)=x3+4x2+6x+9f(x) = x^3 + 4x^2 + 6x + 9f(x)=x3+4x2+6x+9
Show that f(x)f(x)f(x) has a root between -3.5 and -2.5
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=−(6x+9x2+4)\displaystyle x = -\left(\frac{6x+9}{x^2} + 4\right)x=−(x26x+9+4)
Use the iteration formula xn+1=−(6xn+9xn2+4)\displaystyle x_{n+1} = -\left(\frac{6x_n+9}{x_n^2} + 4\right)xn+1=−(xn26xn+9+4) with x0=−3.5x_0 = -3.5x0=−3.5 to find, to 3 decimal places, the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3.
By choosing a suitable interval, prove that α=−3.000\alpha = -3.000α=−3.000 to 3 decimal places
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.