Questions: Find the locations and values of all relative extrema for the function with the graph below.

Solution Steps

To find the relative extrema, we need to look for points on the graph where the function changes direction. These points are typically where the slope of the function changes from positive to negative (relative maximum) or from negative to positive (relative minimum).

From the graph, we can see that the function decreases until it reaches the point (2, 2), and then it starts increasing. Therefore, the point (2, 2) is a relative minimum.

From the graph, we can see that the function increases until it reaches the point (0, 6), and then it starts decreasing. Therefore, the point (0, 6) is a relative maximum.

Final Answer