Using critical values and endpoints to determine the extrema of a polynomial

The video tutorial explains how to find critical numbers by differentiating a function and setting the derivative equal to zero. It then discusses testing endpoints and critical numbers to find extrema. The instructor evaluates the function at various points to determine the absolute maximum and minimum values, presenting them as coordinate points.

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

• Evaluate the function at endpoints

• Integrate the function

• Differentiate the function and set the derivative to zero

• Find the second derivative

After differentiating the function, what should you do next to find critical numbers?

• Find the second derivative

• Solve the equation for x

• Integrate the derivative

• Evaluate the function at x = 0

Why is it important to test both endpoints and critical numbers?

• To find the average value of the function

• To determine the slope of the function

• To calculate the area under the curve

• To identify the extrema of the function

What is the value of the function at x = 0?

• -1

• 0

• 1

• 16

How can the absolute maximum and minimum be expressed?

• As coordinate points

• As a single number

• As a derivative

• As a range of values