Extrema,Increasing, and Decreasing

Front

What is a relative maximum in a function?

Back

A relative maximum is a point in the domain of a function where the function value is greater than the values of the function at nearby points.

Front

What is a relative minimum in a function?

Back

A relative minimum is a point in the domain 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 be increasing on an interval?

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 the function value at the first point.

Front

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

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 the function value at the first point.

Front

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

Back

To find intervals of increase and decrease, calculate the derivative of the function, set it to zero to find critical points, and test the sign of the derivative in the intervals defined by these critical points.

Front

What is the first derivative test?

Back

The first derivative test is a method used to determine whether a critical point is a relative maximum, relative minimum, or neither by analyzing the sign of the derivative before and after the critical point.

Front

What is an absolute maximum?

Back

An absolute maximum is the highest point over the entire domain of a function.

Front

What is an absolute minimum?

Back

An absolute minimum is the lowest point over the entire domain of a function.

Front

What is the difference between relative and absolute extrema?

Back

Relative extrema are points where the function is higher or lower than nearby points, while absolute extrema are the highest or lowest points over the entire function.

Front

What is a critical point?

Back

A critical point is a point in the domain of a function where the derivative is zero or undefined.