To find the instantaneous rate of growth of the culture at 2 minutes, we need to find the derivative of the function f(t) with respect to t and evaluate it at t = 2.

The derivative of f(t) = 71t^3 + 63 is given by:

f’(t) = 3 * 71t^2

To find the instantaneous rate of growth at t = 2, we substitute t = 2 into the derivative:

f’(2) = 3 * 71(2)^2 = 3 * 71(4) = 3 * 284 = 852

Therefore, the instantaneous rate of growth of the culture at 2 minutes is 852 milligrams per minute.