FC Increasing and Decreasing Practice

Front

What is an interval of increase in a function?

Back

An interval of increase is a range of x-values where the function's output (f(x)) is rising as x increases.

Front

What is an interval of decrease in a function?

Back

An interval of decrease is a range of x-values where the function's output (f(x)) is falling as x increases.

Front

How do you identify local maxima on a graph?

Back

Local maxima are points where the function value is higher than the values of the function at nearby points.

Front

What does the notation (-∞, 0) ∪ (2, ∞) represent?

Back

This notation represents two intervals: all values less than 0 and all values greater than 2.

Front

What is the significance of critical points in a function?

Back

Critical points are where the derivative is zero or undefined, indicating potential local maxima, minima, or points of inflection.

Front

How can you determine if a function is increasing or decreasing on an interval?

Back

You can determine this by analyzing the sign of the derivative: if f'(x) > 0, the function is increasing; if f'(x) < 0, it is decreasing.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints (e.g., (a, b)), while closed intervals do include their endpoints (e.g., [a, b]).

Front

What does it mean for a function to have a local maximum at a point?

Back

It means that at that point, the function's value is greater than the values of the function at points immediately surrounding it.

Front

How do you find the intervals of increase and decrease from a graph?

Back

You can find these intervals by observing where the graph rises (increasing) or falls (decreasing) as you move from left to right.

Front

What is the role of the first derivative in determining increasing/decreasing intervals?

Back

The first derivative indicates the slope of the function; positive values indicate increasing intervals, while negative values indicate decreasing intervals.