CPM Homework Help : CALC Problem 3-148

Sketch the graph of a function continuous over all real numbers that satisfies both of the following properties.

Hint 1:

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

Hint 2:

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

Hint 3:

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

Hint 4:

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

Hint 5:

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