Applying the first derivative test to a polynomial to determine the increasing and decreasing

The video tutorial covers the importance of ensuring a function is continuous and differentiable before analyzing its behavior. It explains how to find the derivative and critical values, and how to analyze intervals using test points. The tutorial emphasizes the importance of clear communication in mathematical writing, encouraging students to articulate their findings in words rather than just symbols.

How can asymptotes affect the continuity of a function on a given interval?

What is the importance of showing work when solving for critical values?

Describe how to identify a relative maximum of a function.