f(x) = 1 − x − cos (x²)
a. Show that the equation f(x) = 0 has a root α in the interval 1.4 < α < 1.5.

b. Using x₀ = 1.4 as a first approximation to α, apply the Newton–Raphson procedure once to f(x) to find a second approximation to α, giving your answer to 3 decimal places.

c. By considering the change of sign of f(x) over an appropriate interval, show that your answer to part b is correct to 3 decimal places.