Question

What does the notation f prime of x mean?

Answer 1

F ' (x) represents the derivative of a function. Primarily used in calculus, the derivative is the rate of change on a nonlinear system. 
If you recall from linear algebra, lines have a slope, as they have a constant rate of change (and the slope was defined as 'm' in y=mx+b). 
Curved systems (like parabola and other complex functions) have varying rates of change, requiring the use of the derivative of a function.