identify the local minimum for the function shown.\na (2, 1)\nb (1, 2)\nc (-2, -1)\nd (-1, -2)

Explanation:

Step1: Recall local - minimum definition

A local minimum is a point on the graph where the function value is less than or equal to the values of the function at nearby points.

Step2: Observe the graph

By looking at the given graph, we find the point where the function changes from decreasing to increasing.

Step3: Identify the local - minimum point

The function changes from decreasing to increasing at the point $(-1,-2)$.

Answer:

D. $(-1,-2)$