Question

question
the given function ( f(x) ) is defined on the interval ( -9, 9 ) and represented by the graph below. for the circled point, select all that apply.

answer (choose 1 out of 5)

• the point is an absolute maximum
• the point is an absolute minimum
• the point is a relative maximum
• the point is a relative minimum
• the point is neither an absolute nor a relative extremum

Explanation:

To determine the nature of the circled point, we analyze the definitions of absolute and relative extrema:

• Absolute maximum: The highest point on the entire interval \([-9, 9]\). The circled point is not the highest (e.g., the left - side peak is higher).
• Absolute minimum: The lowest point on the entire interval. The circled point is not the lowest (the bottom - most point on the y - axis is lower).
• Relative maximum: A point higher than its immediate neighbors. The circled point is higher than the points around it (to the left and right in its local region), so it is a relative maximum.
• Relative minimum: A point lower than its immediate neighbors. The circled point is not lower than its neighbors.
• Neither: Since it is a relative maximum, this is incorrect.

Answer:

The point is a relative maximum