Question

practice
examples 1 and 2
identify and estimate the x - and y - values of the extrema. round to the nearest tenth if necessary.
1.
2.
3.
4.

1. landscapes jalen uses a graph of a function to model the shape of two hills in the background of a videogame that he is writing. estimate the x - coordinates at which the relative maxima and relative minima occur. describe the meaning of the extrema in the context of the situation.

examples 3 - 5

Explanation:

Step1: Observe the graph for extrema

Look for peaks (maxima) and valleys (minima).

Step2: Estimate x - values

Read the x - coordinates of the extrema from the graph grid.

Step3: Estimate y - values

Read the y - coordinates of the extrema from the graph grid.

For problem 1:

• Local minimum: Estimated x - value around - 1.5, y - value around - 4.
• Local maximum: Estimated x - value around 0, y - value around 0.

For problem 2:

• Local minimum: Estimated x - value around - 1, y - value around - 4.
• Local maximum: Estimated x - value around 1, y - value around 4.

For problem 3:

• Local minimum: Estimated x - value around 0, y - value around - 3.

For problem 4:

• Local minimum: Estimated x - value around - 1.5 and 1.5, y - value around - 2.
• Local maximum: Estimated x - value around 0, y - value around 2.

For problem 5:

• Relative maxima: Estimated x - coordinates around - 3 and 3. These represent the horizontal positions of the tops of the hills in the video - game landscape.
• Relative minima: Estimated x - coordinates around 0. This represents the horizontal position of the valley between the two hills in the video - game landscape.

Answer:

1. Local minimum: x ≈ - 1.5, y ≈ - 4; Local maximum: x ≈ 0, y ≈ 0
2. Local minimum: x ≈ - 1, y ≈ - 4; Local maximum: x ≈ 1, y ≈ 4
3. Local minimum: x ≈ 0, y ≈ - 3
4. Local minimum: x ≈ - 1.5, y ≈ - 2; x ≈ 1.5, y ≈ - 2; Local maximum: x ≈ 0, y ≈ 2
5. Relative maxima: x ≈ - 3, x ≈ 3; Relative minima: x ≈ 0; Maxima represent tops of hills, minima represent valley between hills.