the function $f$ is given by the graph below.\nstep 1 of 2: use the graph to determine the locations and…

the function $f$ is given by the graph below.\nstep 1 of 2: use the graph to determine the locations and type of the local extrema. write dne for all extrema that do not exist. separate multiple answers with a comma, if necessary.

the function $f$ is given by the graph below.\nstep 1 of 2: use the graph to determine the locations and type of the local extrema. write dne for all extrema that do not exist. separate multiple answers with a comma, if necessary.

Answer

Explanation:

Step1: Identify the vertex of the parabola

The graph shows a parabola opening upwards, with its lowest point at $(-2, 2)$.

Step2: Determine the local minimum

A local minimum occurs at the lowest point of a curve in a specific interval. $$x = -2, y = 2$$

Step3: Determine the local maximum

Since the parabola opens upwards infinitely, there are no local maximum points. $$DNE$$

Answer:

Local minimum: $(-2, 2)$ Local maximum: DNE