Question

this question has two parts. first, answer part a. then, answer part b. part a
incorrect
try left. try once more
a. use the given graph to identify and estimate the x- and y-values of the extrema.
relative maxima, relative minima dropdowns and x, y value dropdowns
part b
correct!
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Explanation:

Step 1: Analyze Relative Maximum

To find the relative maximum, we look for the peak of the graph. From the grid, the peak (relative maximum) occurs at \( x = 1 \) (estimating from the graph's position, likely a typo in the original incorrect \( x = 1/2 \); let's correct based on grid). The \( y \)-value at this peak: looking at the grid, if each square is 1 unit, the peak is at \( y = 4 \) (this part was correct). Wait, maybe the original \( x = 1/2 \) was wrong. Let's re - estimate: the vertex of the upper parabola - like part. Let's assume the grid has each square as 1 unit. The relative maximum is at \( x = 1 \) (maybe the original \( 1/2 \) was a miscalculation) and \( y = 4 \).

Step 2: Analyze Relative Minimum

For the relative minimum, we look at the lowest point of the graph (the bottom of the "U" - shaped part). From the grid, the \( x \)-value of the relative minimum: let's see, the bottom is at \( x = 3 \) (not \( x=-3 \), that was incorrect). The \( y \)-value: looking at the grid, the lowest point is at \( y=-3 \) (not \( y = 3 \), that was incorrect). Wait, maybe I misread the graph. Let's re - examine:

Looking at the graph, the left part comes from the bottom, crosses the origin area, has a peak, then a valley (relative minimum), then goes up. Let's count the grid squares. Let's assume the origin \( O \) is at (0,0). The relative maximum: the peak is at \( x = 1 \) (since it's 1 unit to the right of the origin) and \( y = 4 \) (4 units up). The relative minimum: the valley is at \( x = 3 \) (3 units to the right of the origin) and \( y=-3 \) (3 units down).

Wait, maybe the original problem's grid has different scaling. Let's do it properly:

For Relative Maximum:

A relative maximum is a point where the function changes from increasing to decreasing. From the graph, the peak (relative maximum) is at \( x = 1 \) (estimating from the graph's position, the vertex of the upper curve) and \( y = 4 \) (the \( y \)-coordinate of that peak).

For Relative Minimum:

A relative minimum is a point where the function changes from decreasing to increasing. The bottom of the lower curve (the relative minimum) is at \( x = 3 \) (estimating from the graph's position, the vertex of the lower "U" - shaped part) and \( y=-3 \) (the \( y \)-coordinate of that minimum).

Answer:

Relative maxima at \( x = 1 \), \( y = 4 \); Relative minima at \( x = 3 \), \( y=-3 \) (Note: The original answers had incorrect \( x \) and \( y \) for relative minima and possibly \( x \) for relative maxima. The correct estimation is based on the graph's grid - like structure where we count the units from the origin. If the grid has each square as 1 unit, the relative maximum is at \( (1,4) \) and relative minimum is at \( (3, - 3) \))