Intervals of Increasing and Decreasing

Front

What is an interval of increasing for a function?

Back

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

Front

What is an interval of decreasing for a function?

Back

An interval of decreasing for a function is a range of x-values where the function's output (y-value) decreases as x increases.

Front

How do you determine intervals of increasing and decreasing from a graph?

Back

You can determine intervals of increasing and decreasing by observing the slope of the graph: if the slope is positive, the function is increasing; if the slope is negative, the function is decreasing.

Front

What is the derivative of a function used for in relation to increasing and decreasing intervals?

Back

The derivative of a function indicates the slope of the function. If the derivative is positive, the function is increasing; if negative, it is decreasing.

Front

For the function f(x) = x^2 - 4x + 6, what is the critical point?

Back

The critical point occurs where the derivative f'(x) = 0. For this function, the critical point is x = 2.

Front

What are the intervals of increasing for the function f(x) = x^2 - 4x + 6?

Back

The intervals of increasing for this function are (2, ∞).

Front

What are the intervals of decreasing for the function f(x) = x^2 - 4x + 6?

Back

The intervals of decreasing for this function are (-∞, 2).

Front

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

Back

If a function is constant on an interval, it means that the output (y-value) does not change as the input (x-value) changes within that interval.

Front

How can you identify a constant function on a graph?

Back

A constant function on a graph appears as a horizontal line, indicating that the y-value remains the same regardless of the x-value.

Front

What is the significance of the first derivative test?

Back

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