Vertical tangent lines If a function f is continuous ata

QUESTION:

If a function f is continuous at a and \(\lim _{x \rightarrow a}\ |f'(x)|=\infty\), then the curve y = f(x) has a vertical tangent line at a and the equation of the tangent line is x = a. If a is an endpoint of a domain, then the appropriate one-sided derivative (Exercises 59-60) is used. Use this definition to answer the following questions.

Verify that \(f(x)=x^{1/3}\) has a vertical tangent line at x =0.