Let f(x)=x3−x−1f(x)=x^3-x-1f(x)=x3−x−1.
Show that f(x)=0f(x)=0f(x)=0 has a root between 1.3 and 1.4.
Starting with x0=1.3x_0=1.3x0=1.3, use Newton–Raphson iteration to find x1x_1x1, x2 x_2\,x2 and x3x_3x3. Give each value to six decimal places.
By considering a suitable interval, prove that the root is 1.3247 correct to four decimal places.
125 exam-style questions on CCEA A Level Maths 3.7 Numerical methods (A-level only), covering 3.7.1 Numerical methods (A-level only), 3.7.2 Numerical methods (A-level only), 3.7.3 Numerical methods (A-level only), and 3.7.4 Numerical methods (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.