Increasing, Decreasing and constant Intervals

Front

What are increasing intervals in a function?

Back

Increasing intervals are ranges of x-values where the function's output (y-values) increases as x increases.

Front

What are decreasing intervals in a function?

Back

Decreasing intervals are ranges of x-values where the function's output (y-values) decreases as x increases.

Front

What are constant intervals in a function?

Back

Constant intervals are ranges of x-values where the function's output (y-values) remains the same as x increases.

Front

How do you identify increasing intervals on a graph?

Back

Increasing intervals can be identified on a graph where the slope of the tangent line is positive.

Front

How do you identify decreasing intervals on a graph?

Back

Decreasing intervals can be identified on a graph where the slope of the tangent line is negative.

Front

How do you identify constant intervals on a graph?

Back

Constant intervals can be identified on a graph where the slope of the tangent line is zero.

Front

What is the significance of critical points in determining intervals?

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 the first derivative test?

Back

The first derivative test is a method used to determine whether a critical point is a local maximum, minimum, or neither by analyzing the sign of the derivative before and after the point.

Front

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

Back

If a function is increasing on an interval, it means that for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

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

Back

If a function is decreasing on an interval, it means that for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2).