Function Attributes #2

Front

What is an Absolute Maximum?

Back

The highest point over the entire domain of a function.

Front

What is an Absolute Minimum?

Back

The lowest point over the entire domain of a function.

Front

What is a Relative Maximum?

Back

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

Front

What is a Relative Minimum?

Back

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

Front

How do you identify extrema on a graph?

Back

Look for points where the derivative is zero or undefined, and analyze the behavior around those points.

Front

What does the end behavior of a graph describe?

Back

The behavior of the function as x approaches positive or negative infinity.

Front

What is the significance of the first derivative in finding extrema?

Back

The first derivative indicates the slope of the function; where it equals zero, potential extrema occur.

Front

What is the second derivative test?

Back

A method to determine the concavity of a function and confirm whether a critical point is a maximum or minimum.

Front

What does it mean if a function has no Absolute Maximum?

Back

The function continues to increase indefinitely without reaching a highest point.

Front

What is the difference between Absolute and Relative extrema?

Back

Absolute extrema are the highest or lowest points over the entire domain, while Relative extrema are the highest or lowest points in a local neighborhood.