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-axis) 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-axis) falls as x increases.

Front

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

Back

Look for sections where the graph slopes upwards (increasing) or downwards (decreasing).

Front

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

Back

It represents all values less than 'a' on the x-axis.

Front

What does the notation (a, ∞) represent?

Back

It represents all values greater than 'a' on the x-axis.

Front

What is the significance of critical points in determining intervals?

Back

Critical points are where the function changes from increasing to decreasing or vice versa, helping to identify intervals.

Front

If a function is increasing on (a, b), what can be said about its derivative?

Back

The derivative of the function is positive on the interval (a, b).

Front

If a function is decreasing on (a, b), what can be said about its derivative?

Back

The derivative of the function is negative on the interval (a, b).

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.