Find the critical values of an absolute value function

The video tutorial discusses the concept of absolute value and its representation as a function. It explores graph transformations, including reflections and shifts, and how these affect the graph's appearance. The tutorial also delves into the concept of derivatives, explaining why certain graphs do not have horizontal tangents and identifying critical values where the derivative does not exist.

What transformations are applied to the graph when reflecting it about the X-axis and shifting it to the right?

Describe how the graph looks after applying the transformations mentioned in the text.

Explain the significance of the derivative being set equal to zero in relation to horizontal tangents.

What does it mean when the derivative does not exist at a certain point, and how does this relate to critical values?

What role does the concept of 'corners' play in determining the presence of horizontal tangents?