Question

About vertical tangent
If a point (e.g x=1) is undefined in the original f(x) function, that means it is a vertical asymptote right

so for f'(x), x=1 is the critical number, and it is also undefined
the signs are both positive, which indicates a vertical tangent
but that point is already a Vertical asymptote, so it cant be a vertical tangent

then when will there be a vertical tangent?