The parabola demonstrates that the condition for when the two roots merge is that both the function and its derivative vanish just before both solutions disappear. In the soap film case, given b, this gives us a system of 2 simultaneous equations,rk(d) - b = 0(1),(d) = 0(2),which we can solve for d, k together. However, it's also possible to use a change of variables,d = zk. Then we can use (1) to find,1k2cosh(z) - bsinh(z)Finally, we can substitute k back into (2) to find a closed equation purely for z in terms of b. After solving for z, we can calculate k and then d. Write a function critical_d(b, eps) that takes two input arguments, b and a tolerance eps , and returns the value for d where the stable soap film disintegrates. For full marks, your function should also be vectorised, where it can input a NumPy array of b parameter values, and return an array of the same shape with corresponding values of d