3. $$f ( x ) = x ^ { 2 } + \frac { 3 } { 4 \sqrt { } x } - 3 x - 7 , \quad x > 0$$ A root \(\alpha\) of the equation \(\mathrm { f } ( x ) = 0\) lies in the interval \([ 3,5 ]\).
Taking 4 as a first approximation to \(\alpha\), apply the Newton-Raphson process once to \(\mathrm { f } ( x )\) to obtain a second approximation to \(\alpha\). Give your answer to 2 decimal places.