Question

Can someone help me with this math homework please!

Answer 1

Answers:

• A local maximum occurs over the interval (-2, 0)
• A local minimum occurs over the interval  (0, 2)

This is describing interval notation and not ordered pair notation.

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Explanation:

Plot all of the points on the same xy coordinate grid. See the diagram below. The highest point seems to be point C located at (x,y) = (-1,2) showing that y = 2 is probably the local max. I use "probably" because there might be other values that the table isn't mentioning, due to the nature of continuous functions.

If we strictly go by what the table tells us, then y = 2 is the largest y output. This is considered a local maximum. It's the highest point in this specific region. That region being -2 < x < 0 which translates over to the interval notation (-2, 0). Be sure to not confuse this with ordered pair (x,y) notation, which unfortunately the notation is identical.

The same graph of points also shows us that y = -4 is the smallest y output (point E). This is over the interval 0 < x < 2 which gets us the interval notation (0, 2). Like before, this is not ordered pair notation.