#6 Increasing, Decreasing, Domain, Range, Max, Min

Front

What is the definition of a decreasing function?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, where x1 < x2, the function value at x1 is greater than the function value at x2 (f(x1) > f(x2)).

Front

What is the definition of an increasing function?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, where x1 < x2, the function value at x1 is less than the function value at x2 (f(x1) < f(x2)).

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

How do you determine the intervals where a function is increasing?

Back

To determine where a function is increasing, find the intervals where the derivative of the function is positive.

Front

How do you determine the intervals where a function is decreasing?

Back

To determine where a function is decreasing, find the intervals where the derivative of the function is negative.

Front

What is a local maximum?

Back

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

Front

What is a local minimum?

Back

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

Front

What does it mean for a function to have a maximum or minimum?

Back

A function has a maximum if there exists a point where the function reaches its highest value in a given interval, and a minimum if there exists a point where it reaches its lowest value.

Front

What is the significance of critical points in determining maxima and minima?

Back

Critical points are where the derivative is zero or undefined; they are potential locations for local maxima and minima.