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

Front

What are increasing intervals in a graph?

Back

Increasing intervals are ranges on the x-axis where the function's value (y) rises as x increases.

Front

What are decreasing intervals in a graph?

Back

Decreasing intervals are ranges on the x-axis where the function's value (y) falls as x increases.

Front

How do you identify increasing intervals from a graph?

Back

Look for sections where the graph moves upward from left to right.

Front

How do you identify decreasing intervals from a graph?

Back

Look for sections where the graph moves downward from left to right.

Front

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

Back

The function's value does not change; the graph is a horizontal line.

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 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 use the first derivative test to determine intervals of increase and decrease?

Back

By analyzing the sign of the first derivative: if f'(x) > 0, the function is increasing; if f'(x) < 0, it is decreasing.

Front

What is the role of the second derivative in analyzing intervals?

Back

The second derivative indicates concavity; it helps determine the nature of critical points (maxima or minima).