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.
125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.