### Home > APCALC > Chapter 3 > Lesson 3.4.1 > Problem3-148

3-148.

Sketch the graph of a function that satisfies both of the following properties. Homework Help ✎

• $\lim\limits _ { x \rightarrow 2 ^ { - } } f ^ { \prime } ( x ) = 0$

• $\lim\limits_ { x \rightarrow 2 ^ { + } } f ^ { \prime } ( x ) = \infty$

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.