Increasing and Decreasing Intervals -It's Like a roller coaster

Front

What is an increasing interval in a graph?

Back

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

Front

What is a decreasing interval in a graph?

Back

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

Front

How do you identify increasing intervals on a graph?

Back

Look for sections of the graph where the slope is positive, meaning the graph rises 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, meaning the graph falls from left to right.

Front

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

Back

It means that the function's output does not change as x varies within that interval.

Front

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

Back

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

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 point.

Front

What is the role of the second derivative in analyzing intervals of increase and decrease?

Back

The second derivative indicates the concavity of the function; if it's positive, the function is concave up (increasing), and if negative, concave down (decreasing).

Front

What does the notation (-∞, 1) represent?

Back

It represents an interval that includes all real numbers less than 1, extending indefinitely to the left.

Front

What does the notation (1, ∞) represent?

Back

It represents an interval that includes all real numbers greater than 1, extending indefinitely to the right.