Calculus: We give a checklist for sketching the graph of a function f(x) using the first and second derivatives. As an example, we sketch f(x) = 1/(x-2)^2.

1. Limits 1a - Definition and Basic Concepts
2. Limits 1b - Delta-Epsilon Formulation
3. Limits 1c - Limit Failure
4. Limits 1d - Polynomial and Rational Functions
5. Limits 1e - Compositions and Squeeze Theorem
6. Limits 1f - Trigonometric Functions
7. Examples of Limits
8. Continuity 1a - Definition and Basic Concepts
9. Continuity 1b - Polynomial/Rational Functions and The Extreme Value Theorem
10. Examples of Continuity
11. Fast Solution of Inequality Using Continuity
12. Bisection Method 1
13. Bisection Method 2
14. Vertical Asymptotes 1a
15. Vertical Asymptotes 1b
16. Definition of Tangent Line
17. Example of Tangent Line
18. Definition of Derivative
19. Power Rule for Derivatives
20. Tangent Line to x^2-4x
21. Horizontal Tangent Lines to a Polynomial
22. Derivative of sin(x) and cos(x)
23. Tangent Lines to sin(x)
24. Motion in a Line
25. The Product Rule
26. General Product Rule
27. Power Rule for Rational Exponents
28. The Quotient Rule
29. Trig Derivatives
30. Examples of Trig Derivatives
31. Tangent Lines for sec(x)
32. Tangent Lines for cot(x)
33. The Chain Rule
34. Example of Chain Rule 1 - Basic Examples
35. Example of Chain Rule 2 - Approximation with Tangent Line
36. Example of Chain Rule 3 - Trig Functions
37. Example of Chain Rule 4 - Triple Chain Rule
38. Higher Order Derivatives
39. Graphs and Higher Order Derivatives
40. Implicit Differentiation 1 - Definition and Basic Concepts
41. Implicit Differentiation 2 - Basic Example
42. Implicit Differentiation 3 - Approximation with Tangent Line
43. Implicit Differentiation 4 - Example with Trig Functions
44. Implicit Differentiation 5 - Higher Derivatives
45. Related Rates
46. Example of Related Rates 1
47. Example of Related Rates 2
48. Extreme Value Theorem Using Critical Points
49. Example of Extreme Value Theorem 1
50. Example of Extreme Value Theorem 2
51. Example of Extreme Value Theorem 3
52. Rolle's Theorem
53. Mean Value Theorem
54. Increasing/Decreasing and Derivatives 1
55. Increasing/Decreasing and Derivatives 2
56. Example of Increasing/Decreasing 1
57. Example of Increasing/Decreasing 2
58. Example of Increasing/Decreasing 3
59. First/Second Derivative Test for f(x) = x^4 - 12x^3
60. First/Second Derivative Test for f(x) = sin(x)
61. First/Second Derivative Test for f(x) = x^2 - 6x^{4/3}
62. Concavity and the Second Derivative
63. Concavity for f(x) = sin(x)
64. Concavity for f(x) = (x^2 - 36)/(x-2)
65. Concavity for f(x) = |x^2 - 4x - 12|
66. Example of Limit at Infinity 1
67. Example of Limit at Infinity 2
68. Example of Limit at Infinity 3
69. Checklist for Sketching Functions
70. Graph of f(x) = x^4 - 8x^3
71. Graph of f(x) = (x-2)/(x-1)
72. Graph of f(x) = sin(x) + cos(x)
73. Graph of f(x) = sin(x)/(1+cos(x))
74. Graph of f(x) = x^{4/3} - 8x^{2/3}
75. Optimization 1
76. Optimization 2
77. Optimization 3
78. Optimization - Maximizing Profit
79. Newton's Method 1
80. Newton's Method 2
81. Differentials 1
82. Differentials 2

In this first in a collection of seven series of calculus lessons, Math Doctor Bob (Robert Donley) walks you through the very first steps of differential calculus: Limits; continuity; intermediate value theorem; bisection method; tangent lines; derivatives; optimization; Newton's Method; and differentials.