Graph Analysis: Relative Extrema and Calculator Use

To return to the home screen, press the "Second" button followed by "Quit".
When inputting a value, such as $x = -1.754$ , map it to render the graph correctly.

Always analyze graphs from left to right.
This convention is crucial for correctly identifying increasing or decreasing intervals.
For example, even if a segment appears to be decreasing when viewed from right to left, the standard interpretation requires moving from left to right.

A relative maximum (relative max) represents a "hilltop" or "mountain top" on the graph.
It is the highest point within a specific interval.

A relative minimum (relative min) represents a "valley" or the lowest point in a specific interval.

To find a relative maximum or minimum point on a calculator:
- Go to the point on the graph where you suspect an extremum.
- Select a point slightly to the left of the extremum.
- Select a point slightly to the right of the extremum.
- The calculator will then identify the precise maximum or minimum point within that bounded region.
Troubleshooting: Ensure that the selected left and right boundaries truly surround the peak or valley of the major figure you are trying to analyze. Your selected points should "surround that very top (or bottom) point."
The calculated value for the extremum should be exact and consistent.

The concept of increasing and decreasing intervals will be further explored in subsequent sections (e.g., "Section one, two, or My lab").