Intervals of Increase and Decrease

Front

What is an interval of increase?

Back

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

Front

What is an interval of decrease?

Back

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

Front

How do you determine where a function is increasing or decreasing?

Back

To determine where a function is increasing or decreasing, analyze the function's derivative: if f'(x) > 0, the function is increasing; if f'(x) < 0, it is decreasing.

Front

What does it mean if a function is increasing on the interval (-3, 3)?

Back

It means that for every x-value in the interval (-3, 3), the corresponding y-values of the function are getting larger.

Front

What does it mean if a function is decreasing on the interval (2, 3)?

Back

It means that for every x-value in the interval (2, 3), the corresponding y-values of the function are getting smaller.

Front

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

Back

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

Front

If a function is increasing for x < 3 and decreasing for x > 3, what can be said about x = 3?

Back

x = 3 is a critical point where the function changes from increasing to decreasing, often referred to as a local maximum.

Front

What is the derivative of a function?

Back

The derivative of a function represents the rate of change of the function's output with respect to its input, indicating whether the function is increasing or decreasing.

Front

How can you visually identify intervals of increase and decrease on a graph?

Back

On a graph, intervals of increase are where the curve rises from left to right, while intervals of decrease are where the curve falls from left to right.

Front

What does it mean if a function is increasing on all real numbers?

Back

It means that for every x-value, the function's output is always rising, with no intervals of decrease.