Describe the relationship between the graphs of y = x^2 and y = 3√x. how are they alike? how are they different?

Differences:

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 = 03√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 0The 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 xBoth 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 +inftyThe functions doesnt have a horizontal asymptote nor a vertical one

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