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Why do we call vertical tangent as tangent, doessn't it crosses the curve from one side to the other side of the curve at x=0?

$f(x)=x^{1/3}$

Thanks.

Rajesh Marndi
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    Being vertical is not particularly relevant. You could pose the same question for the horizontal tangent to $f(x)=x^3$ at $x=0$. –  Nov 15 '20 at 08:51
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    Tangent line is the limit of section lines. When it cuts the graph it's called inflexion point. – Berci Nov 15 '20 at 09:23
  • @Berci so there always is a real tangent at an inflection point and also at Cusp. – Rajesh Marndi Nov 15 '20 at 09:37

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