Extrema,Increasing, and Decreasing

Front

What is a global (or absolute) maximum?

Back

The highest point over the entire domain of a function.

Front

What is a global (or absolute) minimum?

Back

The lowest point over the entire domain of a function.

Front

Define increasing interval.

Back

An interval where the function's output values increase as the input values increase.

Front

Define decreasing interval.

Back

An interval where the function's output values decrease as the input values increase.

Front

What does it mean for a function to have an extremum?

Back

An extremum is a point where the function reaches a local maximum or minimum.

Front

How do you identify a global maximum on a graph?

Back

Look for the highest point on the graph within the given domain.

Front

How do you identify a global minimum on a graph?

Back

Look for the lowest point on the graph within the given domain.

Front

What is the first derivative test?

Back

A method to determine where a function is increasing or decreasing by analyzing the sign of its first derivative.

Front

What is the second derivative test?

Back

A method to determine the concavity of a function and identify local maxima and minima.

Front

What is the significance of critical points?

Back

Critical points are where the first derivative is zero or undefined, indicating potential extrema.