Intervals of Increase or Decrease

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 (y-values) 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 (y-values) is falling as x increases.

Front

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

Back

You can determine this by analyzing the derivative of the function: if the derivative is positive on an interval, the function is increasing; if negative, it is decreasing.

Front

What does it mean for a function to be constant on an interval?

Back

A function is constant on an interval if its output (y-values) does not change as x varies within that interval.

Front

What is the significance of critical points in determining intervals of increase or 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

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, local minimum, or neither by analyzing the sign of the derivative before and after the point.

Front

What does the notation (-∞, -3) U (3, ∞) represent?

Back

This notation represents the union of two intervals: all x-values less than -3 and all x-values greater than 3.

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How do you find the intervals of increase or decrease for a polynomial function?

Back

To find intervals of increase or decrease for a polynomial function, take the derivative, find critical points, and test intervals around those points.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What does it mean for a function to be decreasing on the interval (15, 40)?

Back

It means that for every x-value in the interval (15, 40), the function's output (y-value) is lower than it is for any x-value before 15 or after 40.