f(x)=12ln(x)−x2+5x>0f(x) = 12\ln(x) - x^2 + 5 \quad x > 0f(x)=12ln(x)−x2+5x>0
Show that y=f(x)y = f(x)y=f(x) has a stationary point in the interval [2.4,2.5][2.4, 2.5][2.4,2.5]
Starting with x0=2.45x_0 = 2.45x0=2.45, apply the Newton-Raphson procedure twice to find an approximation for the x x\,x coordinate of the stationary point in the interval [2.4,2.5][2.4, 2.5][2.4,2.5]. Give your answer to 3 decimal places.
137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.