x² can be defined over all real numbers, while 3√x only admits positive values for x (or 0). Hence the graph of 3√x starts in x = 0
3√x is increasing in its domain, while x² has an interval where it decreases.
x² has a derivate in every element of its domain, while 3√x doesnt have a derivate in 0
The second derivate of x² is positive for all its values, while the second derivate of 3√x is negative. Hence, the graph is x² is convex while the graph of 3√x is concave.
Similarities:
Both functions are increasing for positive values of x
Both functions have a minimum on the point (0,0)
The rest of the points of the graph are above the x-axis (this means that both functions take positive values besides 0)
If you take limit for x reaching +infty, the result is +infty
The functions doesnt have a horizontal asymptote nor a vertical one
