Explore the concepts of absolute and local minimum and maximum values in calculus through this comprehensive video tutorial. Learn about the extreme value theorem for finding absolute extrema and apply the first derivative test to identify relative maximum and minimum values using sign charts on number lines. Discover techniques for finding critical points and critical numbers of functions. Work through numerous examples and challenging practice problems covering topics such as absolute extrema on closed intervals, graphical examples with open and closed endpoints, cusps, parabolas, vertical asymptotes, and unbounded behavior. Gain proficiency in identifying relative extrema both graphically and analytically for various function types, including quadratic, cubic polynomial, square root, exponential, and rational functions. Master the use of sign charts on number lines to determine relative extreme values and explore techniques of differentiation, including the power rule, product rule, quotient rule, and chain rule derivatives. Read more