Extrema,Increasing, and Decreasing

Front

What is an increasing interval in a function?

Back

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

Front

What is a decreasing interval in a function?

Back

A decreasing interval is a range of x-values where the function's output (y-values) is falling as x increases.

Front

How do you identify the global maximum of a function?

Back

The global maximum is the highest point over the entire domain of the function.

Front

How do you identify the local minimum of a function?

Back

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

Front

What does it mean for a function to have a local maximum?

Back

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

Front

What is the significance of critical points in determining increasing and decreasing 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, local minimum, or neither by analyzing the sign of the derivative before and after the point.

Front

What is the second derivative test?

Back

The second derivative test is a method used to determine the concavity of a function and can help identify local maxima and minima based on the sign of the second derivative.

Front

What is the relationship between the first derivative and the increasing/decreasing behavior of a function?

Back

If the first derivative is positive, the function is increasing; if it is negative, the function is decreasing.

Front

What does it mean for a function to be concave up?

Back

A function is concave up if its second derivative is positive, indicating that the function is curving upwards.