Sections, concepts, and problems - updated through Section 8

Section 1. The Mean-Value Theorem. Rolle's Theorem and the Mean-Value Theorem (MVT).
3, 9, 13, 15, 17, 19, 21, 23 (use IVT to show f has at least one root and Rolle's Thm to show f has at most one root), 35, 45, 47

Section 2. Increasing and decreasing functions. The definition of a function increasing/decreasing on an interval and what that has to do with the first derivative of the function.
1, 13, 21, 27, 31, 33, 35, 39, 41, 45, 49, 57

Section 3. Local extreme values. Local extrema, critical numbers, the First Deriviative Test for extrema and the Second Derivative Test for extrema.
1, 3, 15, 19 (get rid of the absolute value bars first), 23, 25, 31, 35

Section 4. Endpoint and absolute extreme values. Absolute extrema and how to find them.
1, 3, 5, 7, 15, 19, 25, 29, 31, 33, 44, 47

Section 5. Some max-min problems. Applying the ideas of Section 4.4 to "real world" problems.
3, 7, 11, 13, 15, 23

Section 6. Concavity and points of inflection. Concavity of the graph of a function and what it has to do with the second derivative; points of inflection.
1, 7, 15, 19, 21, 27, 35, 45, 47

Section 7. Vertical and horizontal asymptotes; vertical tangents and cusps. Vertical asymptotes and what they have to do with "infinite limits," horizontal asymptotes and what they have to do with "limits at infinity," vertical tangent lines, vertical cusps. As an important side note, to evaluate the limit of a rational function as x approaches plus or minus infinity, divide top and bottom by the highest power of x first .
1, 3, 5, 9, 19, 21, 23, 25, 29, 43, 45, 47, 49

Section 8. Curve sketching. Tying together everything you know about increasing/decreasing, concavity, intercepts, asymptotes, vertical tangent lines, cusps, etc., and using all this information to sketch the graph of the given function.
5, 9, 17, 21, 33, 39, 55, 58

Other Chapters

Chapter 1 | Chapter 2 | Chapter 3 | Chapter 4 | Chapter 5 | Chapter 6