Lecture announcements, Chapter 4, 4.1-4.3, 4.5
Applications of differentiation
Lecture 23, October 29.
4.1, absolute and local extreme values. Fermat's Theorem.
Lecture 24, October 31.
4.1 (concluded): Critical numbers and critical points,
Fermat's Theorem again, absolute extrema on a closed interval.
4.2: The Mean Value Theorem. Rolle's Theorem, with proof.
Lecture 25, November 02.
4.2: The Mean Value Theorem. Statement of the theorem.
Average velocity and instantaneous velocity. If \( f'(x)=0 \) on
an interval I, then \(f\) is constant on I (with proof). Hence if
\(f'=g'\) on I, then \(f\) and \(g\) differ by a constant on I.
Examples and applications
Brief intro to 4.3: reminder about increasing and
decreasing functions.
Lecture 26, November 05.
4.3: How derivatives affect the shape of a graph.
The first derivative. Test for
increasing or decreasing functions, with proofs. Examples. First
derivative test for relative extreama, with examples.
Lecture 27, November 07.
4.3, continued. The second derivative. concavity, inflection
points. Second derivative test. Examples.
4.5. Curve sketching. Guidelines.
