Final answer:
Without the function or specific data points, we cannot calculate or order the derivatives f'(8), f'(-2), and f'(4). Derivatives indicate the instantaneous rate of change of a function which requires a function's expression or adequate data representation.
Step-by-step explanation:
From the information given, we cannot directly determine the values of f'(8), f'(-2), and f'(4) as the functions or data points required to calculate the derivatives are not provided. Derivatives, denoted by f', represent the instantaneous rate of change or the slope of the function f at a given point. Normally, to find these values, one would require either the function itself or a graph/table showing the slopes or rate of changes at various points.
It is important to note that in mathematics, particularly calculus, finding the derivative at a specific point typically involves using rules of differentiation if the function is known, or using numerical methods or graphical analysis if given discrete data points. The description seems to mix up several concepts, including instantaneous velocity in physics and the characteristics of f orbitals in chemistry, which are not directly relevant to calculating the derivative of a function in mathematics.
Without the appropriate function or data, we cannot provide a numerical answer or arrange f'(8), f'(-2), and f'(4) from least to greatest. For a precise answer, we would need the explicit function f(x) or a data set with values of f(x) and their corresponding derivatives at the given points.