Notice that these clues are about $f ^\prime (x)$, not $f(x)$.

Translate: As $x$ approaches $2$ from the right, $f ^\prime (x)$ approaches $+\infty$.

Interpretation: From the right, slope of $f(x)$ gets more and more steep.

Translate: As $x$ approaches $2$ from the left, $f ^\prime (x)$ approaches $0$.

Interpretation: From the left, slope of $f(x)$ gets less and less steep.