HW: What is the deal with those units?

A statement like this is quite common in the scientific literature.
"V = 3.8 h where h is in meters and V is in jules."
An equivalent sentence would be
"V = a h, where a = 3.8 jules/meters."
or
"V = 3.8 jules/meters h"
or
"V = 3.8 J/m h."
The last two are not recommended in your writing, since units and variables can be confused.

Why am I saying this? It is in relation to Problem 7.28. That coefficient in front of x^2 is NOT dimensionless/unitless. Rather its dimension is [U(x)] / [x^2].

Also, note the following definition of the turning points, given in 7.26: The "turning points" for this type of motion can be defined as the minimum and maximum values of x for the motion. What does this mean? Let me give you an artificial everyday example. Say, you are hiking by walking forward or backward only. Assume that the altitude changes on your path, so you are also going up and down as you go forward and backward. Say, you go a certain distance and at point A, you turn around. You then go some distances and at point B, you turn around. You repeat this... (because here "you" are not a real person but a roller coaster car or a pendulum or something of that sort). If one uses an x-y coordinate system, where x measures the horizontal position and y measures the vertical position, then the x values of A and B define the turning points of the motion. A and B are collectively minimum and maximum values of the x values covered by your motion, although it is not possible to say which is minimum and which is maximum, since that depends on the choice of the axis.