Applications of Derivatives

Front

What are absolute extrema?

Back

Absolute extrema are the highest and lowest values of a function on a given interval.

Front

How do you find the absolute extrema of a function?

Back

To find absolute extrema, evaluate the function at critical points and endpoints of the interval.

Front

What is a limit in calculus?

Back

A limit is the value that a function approaches as the input approaches a certain point.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the function value at the second point is greater than at the first.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points in that interval, the function value at the second point is less than at the first.

Front

What is a relative maximum?

Back

A relative maximum is a point where the function value is higher than all nearby points.

Front

What is a relative minimum?

Back

A relative minimum is a point where the function value is lower than all nearby points.

Front

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

Back

To determine where a function is increasing or decreasing, analyze the sign of the derivative.

Front

What is the first derivative test?

Back

The first derivative test is a method to determine relative extrema by checking the sign of the derivative before and after critical points.

Front

What is a critical point?

Back

A critical point is where the derivative is zero or undefined.