How to find the extrema using the EVT

The video tutorial explains how to find critical values of a function within a given interval. It discusses the continuity of the function and applies the Extreme Value Theorem to determine where maximum and minimum values occur. The process of finding the derivative using the power rule is demonstrated, followed by identifying critical values where the derivative is zero or undefined. Finally, the function is evaluated at critical points and endpoints to determine extrema.

What is the function f(x) discussed in the video?

• f(x) = 3x - 2 times the cube root of x

• f(x) = 3x + 2 times the square root of x squared

• f(x) = 2x - 3 times the cube root of x squared

• f(x) = 2x + 3 times the square root of x

Why does the Extreme Value Theorem apply to the function f(x)?

• Because the function is differentiable everywhere

• Because the function is not continuous

• Because the function is continuous on the interval

• Because the function has no critical values

What is the derivative of the function f(x) used to find?

• The points where the function is undefined

• The critical values where the derivative is zero or undefined

• The points where the function is continuous

• The maximum and minimum values directly

What is a critical value of the function f(x) where the derivative does not exist?

• x = 1

• x = -1

• x = 0

• x = 2

Which of the following is an endpoint of the interval discussed?

• x = 1

• x = 3

• x = 0

• x = -1

What is the minimum value of the function f(x) on the interval?

• -16

• 0

• -28

• 28

At which point does the function f(x) have a maximum value?

• x = -8

• x = 1

• x = 3

• x = 0