Question

identify and estimate the x- and y-values of the extrema. round to the nearest tenth if necessary.
relative maximum at ( , 4 )
minimum at ( 2 , -4) and (2, -4)

Explanation:

Step1: Analyze the graph's symmetry

The graph is symmetric about the y - axis (since it's a vertical line \(x = 0\)). For a function symmetric about the y - axis, if \((x,y)\) is a point on the graph, then \((-x,y)\) is also on the graph.

Step2: Find the relative maximum

The relative maximum is at the peak of the middle curve. From the graph, the peak is on the y - axis (\(x = 0\)) and the y - value is 4 (as given in the box for the y - coordinate of the relative maximum). So the relative maximum is at \((0,4)\).

Step3: Find the minima

The minima are at the bottom of the two "valleys" of the graph. Due to symmetry about the y - axis, if one minimum is at \((2,-4)\), the other should be at \((- 2,-4)\) (because for a point \((x,y)\) on the graph, \((-x,y)\) is also on the graph when symmetric about y - axis).

Answer:

Relative maximum at \((0, 4)\)
Minimum at \((-2, -4)\) and \((2, -4)\)