question 8 of 11, step 1 of 2\n4/15\ncorrect\nstep 1 of 2: use the graph to determine the locations and type…

question 8 of 11, step 1 of 2\n4/15\ncorrect\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.

question 8 of 11, step 1 of 2\n4/15\ncorrect\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: Understand local extrema

Local extrema are points where the function changes from increasing to decreasing (local maximum) or from decreasing to increasing (local minimum).

Step2: Analyze the graph

The graph is a parabola opening upwards. It has a single local - minimum at the vertex.

Step3: Identify the vertex

The vertex of the parabola is at the point $(0,0)$. Since the parabola opens upwards, this is a local minimum.

Answer:

Local minimum at $(0,0)$