f(x) = x 2 - 4/x + 6x 10, x 0. a. Use differentiation to find f'(x). The root, , of the equation

f(x) = x² - 4/x + 6x − 10, x ≠ 0.

a. Use differentiation to find f'(x).  The root, α, of the equation f(x) = 0 lies in the interval [−0.4, −0.3].

b. Taking −0.4 as a first approximation to α, apply the Newton–Raphson process once to f(x) to obtain a second approximation to α. Give your answer to 3 decimal places.