CPM Homework Help : CALC Problem 3-137

For the absolute value function shown below, something interesting happens to the tangent of the function at $x = 2$ . Can you draw more than one tangent at $x = 2$ ? Do you think this function has any valid tangents at $x = 2$ ?

Hint 1:

Consider the slope as $x→2^−$ and then consider the slope as $x→2^+$ .

Hint 2:

From the left, the slope appears to be $−1$ .

Hint 3:

From the right, what does the slope appear to be?