Understanding Extrema of a Quadratic Function

The video tutorial explains how to find the maximum and minimum values of a quadratic function on a closed interval. It covers the process of identifying critical numbers by taking the derivative and setting it to zero, evaluating the function at these critical points and the interval endpoints, and determining the extrema. The tutorial also demonstrates using a graphing calculator to verify results and provides a visual confirmation through graph analysis.

What is the function given in the video for finding extrema?

• f(x) = x^2 - 2x + 1

• f(x) = 3x^2 + 5x - 7

• f(x) = 2x^2 - 4x + 6

• f(x) = 4x^2 - 10x + 8

What is the first step in finding the absolute extrema of a function on a closed interval?

• Graph the function

• Find the critical numbers

• Calculate the second derivative

• Evaluate the function at the endpoints

What is the derivative of the function f(x) = 4x^2 - 10x + 8?

• 4x + 10

• 8x + 10

• 4x - 10

• 8x - 10

How do you find the critical numbers of a function?

• Graph the function

• Set the second derivative equal to zero

• Set the first derivative equal to zero

• Evaluate the function at the endpoints

What is the critical number found for the function f(x) = 4x^2 - 10x + 8?

• x = 3/2

• x = 1

• x = 2

• x = 5/4

What is the value of f(5/4) for the function f(x) = 4x^2 - 10x + 8?

• 7/4

• 3/4

• 5/4

• 1/4

What is the maximum value of the function on the closed interval [0, 5]?

• 10

• 8

• 7/4

• 58

At which point does the maximum value occur for the function on the interval [0, 5]?

• x = 5

• x = 0

• x = 5/4

• x = 2

What is the minimum value of the function on the closed interval [0, 5]?

• 58

• 5/4

• 8

• 7/4

At which point does the minimum value occur for the function on the interval [0, 5]?

• x = 0

• x = 5/4

• x = 5

• x = 2