Extrema and Increasing/Decreasing

Front

What is an extremum in a graph?

Back

An extremum is a point on a graph where the function reaches a maximum or minimum value.

Front

Define increasing interval.

Back

An increasing interval is a range of x-values where the function's output (y-value) is rising as x increases.

Front

Define decreasing interval.

Back

A decreasing interval is a range of x-values where the function's output (y-value) is falling as x increases.

Front

What does it mean if a function is increasing on an interval?

Back

It means that for any two points in that interval, the function's value at the second point is greater than at the first point.

Front

What does it mean if a function is decreasing on an interval?

Back

It means that for any two points in that interval, the function's value at the second point is less than at the first point.

Front

How do you identify increasing intervals on a graph?

Back

Look for sections of the graph where the slope is positive (rising from left to right).

Front

How do you identify decreasing intervals on a graph?

Back

Look for sections of the graph where the slope is negative (falling from left to right).

Front

What is a local maximum?

Back

A local maximum is a point where the function value is higher than all nearby points.

Front

What is a local minimum?

Back

A local minimum is a point where the function value is lower than all nearby points.

Front

What is the difference between local and global extrema?

Back

Local extrema are the highest or lowest points in a specific interval, while global extrema are the highest or lowest points over the entire domain of the function.