Increasing and Decreasing Intervals

Front

What is an increasing interval in a function?

Back

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

Front

What is a decreasing interval in a function?

Back

A decreasing interval is a range of x-values where the function's output (y-values) is falling 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 (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 (the graph falls from left to right).

Front

What is a maximum value in a function?

Back

A maximum value is the highest point on the graph of a function, where the function changes from increasing to decreasing.

Front

What is a minimum value in a function?

Back

A minimum value is the lowest point on the graph of a function, where the function changes from decreasing to increasing.

Front

What does it mean if a function has a maximum at (2, 0)?

Back

It means that at x = 2, the function reaches its highest value of 0.

Front

What is the significance of critical points in a function?

Back

Critical points are where the derivative is zero or undefined; they help identify local maxima and minima.

Front

How can you determine if a critical point is a maximum or minimum?

Back

Use the first derivative test: if the derivative changes from positive to negative, it's a maximum; if it changes from negative to positive, it's a minimum.

Front

What is the first derivative of a function?

Back

The first derivative represents the rate of change of the function and helps identify increasing and decreasing intervals.