Key Feat. 2: Quick Review

Front

What is the positive interval of a function?

Back

The positive interval of a function is the range of x-values for which the function's output (y-value) is greater than zero.

Front

Define extrema in the context of a graph.

Back

Extrema refer to the maximum and minimum values of a function on a given interval. They can be local (within a small region) or global (over the entire domain).

Front

What is a decreasing interval of a function?

Back

A decreasing interval is a range of x-values where the function's output decreases as x increases.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

What is the significance of positive intervals in functions?

Back

Positive intervals indicate where the function's output is above the x-axis, which is important for understanding the function's behavior and applications.

Front

How do you identify the maximum points on a graph?

Back

Maximum points can be identified by finding the highest y-values in a given interval, often occurring at critical points where the derivative is zero or undefined.

Front

How do you identify the minimum points on a graph?

Back

Minimum points can be identified by finding the lowest y-values in a given interval, often occurring at critical points where the derivative is zero or undefined.

Front

What is the relationship between increasing and decreasing intervals?

Back

Increasing and decreasing intervals are complementary; a function can only be increasing or decreasing in a given interval, and they help define the overall shape of the graph.

Front

What is the role of critical points in determining intervals of increase or decrease?

Back

Critical points, where the derivative is zero or undefined, help identify where a function changes from increasing to decreasing or vice versa.

Front

Explain the concept of local maxima and minima.

Back

Local maxima and minima are points where a function reaches a highest or lowest value within a specific neighborhood, not necessarily the highest or lowest overall.