1．（i） $$f ( x ) = x ^ { 3 } + 4 x - 6$$ （a）Show that the equation \(\mathrm { f } ( x ) = 0\) has a root \(\alpha\) in the interval［1，1．5］
（b）Taking 1.5 as a first approximation，apply the Newton Raphson process twice to \(\mathrm { f } ( x )\) to obtain an approximate value of \(\alpha\) ．Give your answer to 3 decimal places． Show your working clearly．
（ii） $$g ( x ) = 4 x ^ { 2 } + x - \tan x$$ where \(x\) is measured in radians． The equation \(\mathrm { g } ( x ) = 0\) has a single root \(\beta\) in the interval［1．4，1．5］
Use linear interpolation on the values at the end points of this interval to obtain an approximation to \(\beta\) ．Give your answer to 3 decimal places．