Definition:Vertical Tangent Line

Definition
Let $P = (c, f \left({c}\right))$ be a point on the graph of a real function $f$. The vertical line $x = c$ is a vertical tangent line to the graph of $f$ at $P$ iff any of the following hold:


 * $f$ is right continuous at $c$ and $\displaystyle \lim_{x \to c ^+} f^{\prime} \left({x}\right) = +\infty$


 * $f$ is right continuous at $c$ and $\displaystyle \lim_{x \to c ^+} f^{\prime} \left({x}\right) = -\infty$


 * $f$ is left continuous at $c$ and $\displaystyle \lim_{x \to c ^-} f^{\prime} \left({x}\right) = +\infty$


 * $f$ is left continuous at $c$ and $\displaystyle \lim_{x \to c ^-} f^{\prime} \left({x}\right) = -\infty$