Calculate the most developing wave number in the Eady problem

mum.m

#!/usr/bin/env octave -qf
function y = f(x)
# the maximum of kci = sqrt((mu/2 - tanh mu/2)(mu/2 - cot mu/2)) is found by
# finding the zero of the derivative of the inside of sqrt.
  y = x - (tanh(0.5*x) + coth(0.5*x)) - 0.5 * x * (1/(cosh(0.5*x))^2 - 1/(sinh(0.5*x))^2);
endfunction
format long
fsolve("f", 3.2)