The video tutorial covers the concepts of continuity and differentiability of a function on a given interval. It explains how to find the derivative, identify critical values, and create test intervals. The tutorial further analyzes the behavior of the function on these intervals and discusses the conditions for relative extrema, concluding that no maximum or minimum occurs at the critical point due to the derivative's behavior.

What is the derivative of the function F(x) given in the video?

• x^3

• 2x^3

• 3x

• 3x^2

What is identified as the critical value of the function?

• x = 0

• x = 3

• x = 1

• x = -1

How are test intervals defined in the video?

• Using open intervals only

• Using closed intervals only

• Using neither open nor closed intervals

• Using both open and closed intervals

What is the behavior of F(x) on the interval (-3, 0)?

• Undefined

• Increasing

• Decreasing

• Constant

Why does no maximum or minimum occur at x = 0?

• Because F'(x) is zero

• Because F'(x) is positive on both sides of x = 0

• Because F'(x) is negative on both sides of x = 0

• Because F(x) is not continuous