Extrema and Increasing Decreasing Intervals

Front

What are increasing intervals in a graph?

Back

Increasing intervals are ranges on the graph where the function's value rises as the input value increases.

Front

What are decreasing intervals in a graph?

Back

Decreasing intervals are ranges on the graph where the function's value falls as the input value increases.

Front

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

Back

To identify increasing and decreasing intervals, look for sections of the graph where the slope is positive (increasing) or negative (decreasing).

Front

What is an extremum in the context of a graph?

Back

An extremum is a point on the graph 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 the values of the function at nearby points.

Front

What is a local minimum?

Back

A local minimum is a point where the function value is lower than the values of the function at nearby points.

Front

How can you find the extrema of a function?

Back

Extrema can be found by analyzing the first derivative of the function and identifying critical points where the derivative is zero or undefined.

Front

What is the significance of critical points in a graph?

Back

Critical points are significant because they are potential locations for local maxima, minima, or points of inflection.

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points in that interval, the function value at the second point is greater than at the first.

Front

What does it mean for a function to be decreasing on an interval?

Back

A function is decreasing on an interval if, for any two points in that interval, the function value at the second point is less than at the first.