This calculus video tutorial explains how to find the absolute minimum and maximum values as well as the local max and local min. It explains the extreme value theorem for finding absolute extrema and discusses the first derivative test to identify relative maximum and minimum values using a sign chart on a number line. It also discusses how to find the critical points or critical numbers of a function. This video contains plenty of examples and difficult / hard practice problems. Here is a list of topics:
1. Absolute Extrema - Absolute Max and Min on a Closed Interval
2. Extreme Value Theorem
3. Graphical Examples With Open and Closed Endpoints / Circles
4. Cusps, Parabola, Vertical Asymptote and Unbounded Behavior
5. How to Identify The Critical Points or Critical Numbers of a Function - f'(c)=0 or f'(c) does not exist
6. First Derivative Test - If the slope of the function or the sign of f'(x) changes from negative to positive - it's a local minimum value. If it changes from positive to negative - it's a relative maximum
7. Identify absolute extreme values - max and min on a closed interval using the endpoints a making an x y table of values
8. f'(c)=0 at local max and local min - slope of horizontal tangent line is zero
9. Identifying Relative Extrema Graphically and Analytically
10. Local Max and Min of Quadratic Functions, Cubic Polynomial Functions, Square Root Functions, Cusp, Exponential Fractions, and Rational Functions
11. Using a Sign Chart on a Number line to identify the relative extreme values
12. Absolute Extrema - Local Minima and Relative Maxima
13. Techniques of Differentiation - Power Rule, Product Rule, Quotient Rule, and Chain Rule Derivatives
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