Sections, concepts, and problems

Section 1. Tangent lines and the derivative at a point. The definition of the derivative at a point and what it has to do with the slope of a line.
4, 8, 15, 18, 21, 27, 41, 46, 49, 51, 57, 60, 69, 72, 78, 82

Section 2. The derivative as a rate of change. Average and instantaneous rates of change and what they have to do with the derivative.
5, 7, 10, 11, 24, 26, 33, 35

Section 3. Differentiability. Differentiability from algebraic/geometric viewpoints and what differentiability has to do with continuity.
1, 5, 10 - 13, 18, 19, 25, 27

Section 4. The derivative as a function. The definition of the derivative function, what its graph has to do with the graph of the original function, higher-order derivatives, and some applications to physics.
1, 7, 8, 12, 13, 23, 28, 38, 54, 56, 58, 67, 68

Section 5. Basic differentiation rules. Some theorems that will make it easier to calculate derivatives.
11, 18, 21, 23, 25, 40, 45, 51, 53, 60, 65, 71

Section 6. Three theorems about tangent lines. A theorem with no name that will help you find local extrema, Rolle's Theorem, and the Mean Value Theorem (MVT).
1, 2, 6, 7, 13, 15, 18-21, 25, 27, 28, 33-35, 40, 50, 54, 60, 63

Section 7. The first derivative and function behavior. What the first derivative has to do with intervals of increase/decrease.
3, 4, 6, 11, 14, 17 (see pg 77 for the definition of "inflection point"), 22, 26, 27, 33, 42, 45

Section 8. The second derivative and function behavior. What the second derivative has to do with intervals of concavity.
2, 5, 9, 11, 12, 14, 18, 25, 30, 33, 42, 44, 52, 54, 65, 66, 69

Other Chapters

Chap 0 | Chap 1 | Chap 2 | Chap 3 | Chap 4 | Chap 5 | Chap 6