Let f(x) = x3 - 2x - 7,
(a) show that a root of this function lies in the interval (1, 3),
(b) Determine the equation of the tangent line to this curve at x =2 and determine its x-intercept.
(c) Determine the equation of the tangent line to the curve at the x-intercept found in (b) and determine the x-intercept of this tangent line.
(d) Determine the equation of the tangent line to the curve at the x-intercept found in (c) and its x-intercept.
(e) Continue the above and produce a root of the given function to six decimal places.