Extrema and Increasing Decreasing Intervals

Front

What is an increasing interval?

Back

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

Front

What is a decreasing interval?

Back

A decreasing interval is a range of x-values over which the function's output (y-values) decreases as x increases.

Front

How do you determine increasing and decreasing intervals from a graph?

Back

To determine increasing and decreasing intervals, observe the slope of the graph: if the slope is positive, the function is increasing; if the slope is negative, the function is decreasing.

Front

What is an extremum?

Back

An extremum is a point in a function where the function reaches a local maximum or minimum value.

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

How can you find extrema using calculus?

Back

Extrema can be found by taking the derivative of the function, setting it to zero, and solving for x to find critical points.

Front

What is the first derivative test?

Back

The first derivative test is a method used to determine whether a critical point is a local maximum, local minimum, or neither by analyzing the sign of the derivative before and after the critical point.

Front

What does it mean if a function has no extrema?

Back

If a function has no extrema, it means that the function does not have any local maximum or minimum points within the given interval.

Front

How do you identify the number of increasing and decreasing intervals from a function?

Back

To identify the number of increasing and decreasing intervals, analyze the first derivative of the function and determine where it is positive (increasing) and negative (decreasing).