Determine the extrema of a function on a closed interval

The video tutorial explains how to find critical numbers of a function by setting the derivative equal to zero. It discusses the importance of endpoints and critical numbers in determining extrema. The tutorial then demonstrates calculating absolute maximum and minimum values, providing examples and explaining how to express these values as coordinate points.

What is the first step in finding critical numbers of a function?

• Set the derivative equal to zero

• Set the function equal to zero

• Evaluate the function at endpoints

• Find the second derivative

Where do extrema of a function occur?

• Anywhere on the interval

• At the endpoints and critical numbers

• Only at the endpoints

• Only at the critical numbers

What is the purpose of evaluating a function at its critical numbers and endpoints?

• To calculate the derivative

• To identify the extrema

• To determine the slope

• To find the average value

In the given example, what is the absolute minimum value of the function?

• 9

• 3

• 0

• -3

How can absolute extrema be expressed in terms of coordinate points?

• As a range of values

• As a derivative

• As a single number

• As pairs of x and y values