Explain why the function f (x) = =has a vertical asymptote but no vertical tangent

Explain why the function f (x) = =has a vertical asymptote but no vertical tangent.
Clearly x=0 could be the vertical asymptote or tangent.
When ,
When x > 0,
So

However,

Therefore,
when . So x=0 is not a vertical tangent.
However, we do have , when , so x=0 is still a vertical asymptote.

(5) Sketch the graph of the curve for [0,2a). Show all special features such as vertical asymptotes, horizontal asymptotes, cusps, vertical tangents, and intercepts.

, with .
So x=2a is the vertical asymptote.
The intercept is (0,0).

please see the attached file.