It is given that
f(x)=x5+3x2+x−10f(x) = x^5 + 3x^2 + x - 10f(x)=x5+3x2+x−10
Find f′(x)f'(x)f′(x).
The equation f(x)=0f(x) = 0f(x)=0 has a root in the interval [1,1.5][1, 1.5][1,1.5]. Using x0=1.25x_0 = 1.25x0=1.25, apply the Newton-Raphson procedure once to find a second approximation to this root. Give your answer to three 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.