Max/Min, Domain/Range, Increasing/Decreasing

Front

What is a local maximum in a graph?

Back

A local maximum is a point on a graph where the function value is higher than the values of the function at nearby points.

Front

How do you identify local maxima on a graph?

Back

Local maxima can be identified by looking for peaks in the graph where the slope changes from positive to negative.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the function value f(x) also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, the function value f(x) decreases.

Front

What is a constant interval in a graph?

Back

A constant interval is a section of the graph where the function value does not change as x changes.

Front

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

Back

You can determine where a function is increasing or decreasing by analyzing the slope of the graph or using the first derivative test.

Front

What is the significance of critical points in a graph?

Back

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

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.