Question

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

Explanation:

Step1: Analyze Relative Maximum

A relative maximum is a point where the function changes from increasing to decreasing. Looking at the graph, near the y - axis, the peak (relative maximum) seems to be at \(x = 0.5\) (estimating from the grid, assuming each grid square is 1 unit) and \(y = 2\) (estimating the y - value from the graph's height at that x). Wait, actually, let's re - examine. The graph has a peak around \(x = 0.5\) (maybe 0.5) and y - value around 2? Wait, no, let's look at the grid. Let's assume the origin is (0,0). The relative maximum: when x is around 0.5 (maybe 0.5) and y is around 2? Wait, no, let's see the graph. The curve rises, then has a peak, then a valley, then rises again. Let's estimate the coordinates. For the relative maximum: looking at the graph, the x - coordinate of the relative maximum is around 0.5 (since it's near the y - axis, maybe 0.5) and y - coordinate around 2. For the relative minimum: after the peak, the curve goes down to a valley. The x - coordinate of the relative minimum is around 2 and y - coordinate around 1 (estimating from the grid). Wait, maybe more accurately, let's count the grid squares. Let's assume each small square is 1 unit. The relative maximum: x is 0.5 (half a square from y - axis) and y is 2 (two squares up). The relative minimum: x is 2 (two squares to the right of y - axis) and y is 1 (one square up from x - axis). Wait, maybe I made a mistake. Let's re - estimate. The relative maximum: when the function reaches a local high. Looking at the graph, the peak is at (0.5, 2) approximately. The relative minimum: after the peak, the function dips to a local low at (2, 1) approximately? Wait, no, maybe the x - coordinate for relative maximum is 0 (wait, no, the graph crosses the y - axis, but the peak is a bit to the right of y - axis). Wait, maybe the relative maximum is at (0.5, 2) and relative minimum at (2, 1). Wait, let's check again.

Wait, maybe the correct estimation: relative maximum at (0.5, 2) and relative minimum at (2, 1). Wait, no, let's see the graph structure. The function comes from the bottom left, crosses the y - axis, then has a peak (relative maximum) at x≈0.5, y≈2, then goes down to a valley (relative minimum) at x≈2, y≈1, then goes up again.

Step2: Analyze Relative Minimum

A relative minimum is a point where the function changes from decreasing to increasing. So after the relative maximum, the function decreases to a point and then increases. So the x - value of the relative minimum is around 2 (since it's two units to the right of the origin) and y - value around 1 (one unit above the x - axis).

Answer:

Relative maximum at \((0.5, 2)\)
Relative minimum at \((2, 1)\)

(Note: The estimations are based on the grid - like graph provided. If the grid size is different, the values may vary slightly, but this is a reasonable estimation from the given graph structure.)