In this video, Krista King from integralCALC Academy explains an applied optimization example where we find two real numbers with difference 20 and minimum possible product.

1. Vertical Line Test Overview
2. Domain and Range
3. Finding Values and Domain and Range from a Graph
4. Equation Modeling
5. Modeling the Equation of a Piecewise Defined Function from its Graph
6. Sketching a Graph from a Story Problem
7. Determining if a Function is Even, Odd or Neither
8. How to Classify Functions
9. Equation of the Line in Slope-intercept Form
10. Equation of a Line in Point-slope Form
11. Least Squares Line
12. Finding the Inverse of a Function
13. Sketch the Graph of a Parabola
14. Finding the Center and Radius of the Circle
15. Sketch the Graph of a Circle
16. Combinations of Functions and their Domains
17. Composite Functions
18. Composite Functions and their Domains
19. Describing Transformations Algebraically
20. Graphing Transformations
21. Using Transformations to Sketch a Graph
22. Determine Whether a Function is 1 to 1
23. Find the Inverse of a Function and Sketch its Graph
24. Finding the Linear Function Given Two Points on its Inverse
25. Use Laws of Logarithms to Simplify a Logarithmic Function
26. Use the Quadratic Formula to Find Roots of the Function
27. Completing the Square of a Quadratic Function
28. Polynomial Long Division for Rational Functions
29. Hyperbolic Identities
30. Limits: Substitution Method
31. Limits: Factoring Method
32. Limits: Conjugate Method
33. Use Limit Laws to Evaluate Limits of Combination Functions
34. Limits: Crazy Graphs
35. Limits at Infinity
36. Infinite Limits
37. Limits: Trigonometric (Example 2)
38. Limits: One-Sided
39. How to Prove that the Limit Does Not Exist
40. Precise Definition of the Limit
41. Finding Delta from a Graph and the Epsilon-delta Definition of the Limit
42. Squeeze Theorem
43. Limit of an Inequality with Squeeze Theorem
44. Continuity
45. Removable Discontinuity
46. Finding the Value that Makes the Function Continuous
47. Intermediate Value Theorem Overview
48. Intermediate Value Theorem to Prove a Root in an Interval
49. Prove the Equation Has at Least One Real Root
50. How to Calculate the Difference Quotient
51. Power Rule
52. Derivatives of Linear Combinations
53. Product Rule
54. Product Rule - 3+ Functions
55. Quotient Rule
56. Reciprocal Rule
57. Chain Rule
58. Chain Rule for Derivatives with Product Rule
59. Chain Rule for Derivatives with Quotient Rule
60. Chain Rule for Derivatives with Trig Functions
61. Trigonometric Derivatives: Overview
62. Trigonometric Derivatives (Example 1)
63. Derivatives of Inverse Trig Functions: arcsin
64. Derivatives of Inverse Trig Functions: arccot
65. Derivatives of Hyperbolic Functions
66. Derivative of an Inverse Hyperbolic Function
67. Derivatives of Natural Logs (ln)
68. Use Laws of Logarithms to Find the Derivative
69. Derivatives of Exponentials (e^x)
70. Equation of the Tangent Line
71. Differentiability and Vertical Tangent Lines
72. Equation of the Normal Line at a Point
73. Average Rate of Change
74. Implicit Differentiation
75. Use Implicit Differentiation to Find the Equation of the Tangent Line at a Point
76. Use Implicit Differentiation to Find the Second Derivative of y (y'')
77. Half Life
78. Continuously Compounded Interest
79. Sales Decline
80. Linear Approximation in One Variable
81. Linearization of a Function at a Point
82. Critical Points
83. Increasing and Decreasing (Example 1)
84. Concavity and Inflection Points
85. First Derivative Test
86. Second Derivative Test: One Variable
87. Vertical Asymptotes: Overview
88. Horizontal Asymptotes: Basic Overview
89. Horizontal Asymptotes: Further Detail
90. Slant Asymptotes
91. Sketching Graphs (Example 1)
92. Maxima and Minima on a Closed Range
93. Dimensions that Minimize the Surface Area of a Cylinder
94. Largest Area of a Rectangle Inscribed in a Semicircle
95. Dimensions that Maximize the Area of the Rectangle
96. Largest Possible Volume of a Cylinder Inscribed in a Sphere
97. Maximum Volume of a Cone Shaped Cup
98. Dimensions of the Rectangle with Largest Area Inscribed in an Equilateral Triangle
99. Applied Optimization: Two Real Numbers with Difference 20 and Minimum Possible Product
100. Applied Optimization: Area and Margins of a Page
101. Related Rates: Radius of a Balloon and Changing Price
102. Related Rates: Water Level in a Tank
103. Related Rates: Ladder Sliding Down a Wall
104. Related Rates: Distance Between Observer and Airplane
105. Mean Value Theorem
106. Rolle's Theorem
107. Newton's Method
108. L'Hopital's Rule
109. Position Function
110. All About a Particle's Position Function
111. Vertical Motion (Differentiation)
112. Marginal Cost, Revenue and Profit

In this course, Krista King from the integralCALC Academy covers a range of topics in Calculus I, including Precalculus, Limits & Continuity, Derivatives and Applications of Derivatives.