In smoothing spline computations, we need to solve nonlinear equations of the form                           f (t) = i 1 1 + 6tgi = r,  for constants gi > 0. (a) Construct bounds for the root of this...

In smoothing spline computations, we need to solve nonlinear equations of the form

                          f (t) = i 1 1 + 6tgi = r,

 for constants gi > 0.

(a) Construct bounds for the root of this equation based on r and the minimum and maximum of gi.

(b) Recommend a method for solving this nonlinear equation.

(c) Write a function to take r and gi as input and compute the root.