Does the max and min always occur when there is a horizontal tangent

The video tutorial discusses the concepts of maxima and minima in calculus, focusing on the role of derivatives in identifying these extrema. It explains that while derivatives can help find potential extrema, they do not exist at certain points like corners, cusps, or discontinuities. The tutorial emphasizes the importance of understanding these limitations and visualizing extrema on graphs, even when derivatives are not applicable. The session concludes with a cautionary note on relying solely on calculus for finding extrema.

Discuss the significance of horizontal tangents in relation to the derivative.

What is the relationship between the derivative and the identification of maximum and minimum values?

How can visualizing graphs help in understanding the concepts of maxima and minima?

Explain why the derivative might not exist at certain points and how this affects the identification of extrema.

What are some scenarios where extrema can exist even if the derivative does not?