Find $x_{0}$ if you knew that the tangent line is vertical

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Tangent equation at a point is $f'(x_{0})(x-x_{0}) + f(x)$

The problem is that I want to know $x_{0}$ if you knew that the tangent is vertical...so what I need to do?

The slope of the line isn't even 0, it's undefined.

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If the tangent line is vertical at $x_0$, that means $$\lim_{x \to x_0} f'(x) = \pm \infty.$$ So try finding the asymptotes of $f'(x)$ and those should give you the values $x_0$ you're looking for.