Final answer:
The correct answer is option C, 'Greatest less than or equal to x', which identifies the highest possible energy state within a given boundary for a physical system described by an infinite potential well.
Step-by-step explanation:
The correct answer is option C, 'Greatest less than or equal to x'. In a system where the motion is confined and the potential energy is described by an infinite potential well, the maximum energy refers to the highest possible energy state that is still less than or equal to a certain value of x. At the bottom of the potential well, where x = 0, all of the system's energy is kinetic (K = E) since potential energy (U) is zero. Therefore, the term with the greatest energy that still fits the bound of being less than or equal to a value of x is the value that encompasses the system's total energy at that point.
At the bottom of a slope or a potential well, both potential energy and kinetic energy reach their maximum values. This is because when an object is at the bottom, the potential energy is at its highest and the kinetic energy is at its lowest.
For example, imagine a ball rolling down a hill. At the bottom of the hill, the potential energy is at its maximum, since the ball is as low as it can go. At the same time, the kinetic energy is at its minimum because the ball has slowed down as it reached the bottom of the hill.