MindMap Gallery Applications of Derivatives
Mind map of the chapter "Applications of Derivatives in Advanced Mathematics". Derivatives are widely used in mathematics and physics, including concave and convex inflection points. , optimal value, L'Hobida's law, Monotonic extreme values, etc.
Edited at 2024-01-30 19:16:54Avatar 3 centers on the Sully family, showcasing the internal rift caused by the sacrifice of their eldest son, and their alliance with other tribes on Pandora against the external conflict of the Ashbringers, who adhere to the philosophy of fire and are allied with humans. It explores the grand themes of family, faith, and survival.
This article discusses the Easter eggs and homages in Zootopia 2 that you may have discovered. The main content includes: character and archetype Easter eggs, cinematic universe crossover Easter eggs, animal ecology and behavior references, symbol and metaphor Easter eggs, social satire and brand allusions, and emotional storylines and sequel foreshadowing.
[Zootopia Character Relationship Chart] The idealistic rabbit police officer Judy and the cynical fox conman Nick form a charmingly contrasting duo, rising from street hustlers to become Zootopia police officers!
Avatar 3 centers on the Sully family, showcasing the internal rift caused by the sacrifice of their eldest son, and their alliance with other tribes on Pandora against the external conflict of the Ashbringers, who adhere to the philosophy of fire and are allied with humans. It explores the grand themes of family, faith, and survival.
This article discusses the Easter eggs and homages in Zootopia 2 that you may have discovered. The main content includes: character and archetype Easter eggs, cinematic universe crossover Easter eggs, animal ecology and behavior references, symbol and metaphor Easter eggs, social satire and brand allusions, and emotional storylines and sequel foreshadowing.
[Zootopia Character Relationship Chart] The idealistic rabbit police officer Judy and the cynical fox conman Nick form a charmingly contrasting duo, rising from street hustlers to become Zootopia police officers!
Applications of Derivatives
Lópida's Law
Conditions for the application of L'Obitat's Law
Thought
Under certain conditions, the limit is obtained by derivation of the numerator and denominator respectively.
monotonic extremum
Definition of monotonicity
algebraic angle
geometric angle
extremum
Definition: local maximum and minimum
properties of extreme values
extreme value applications
Category: maximum and minimum values
Features: local concept; within the definition domain, there can be multiple extreme values; the tangent level at the extreme point
Existence conditions
Necessary condition: the extreme point must be a stationary point;
Sufficient conditions: first sufficient condition; second sufficient condition
application
Application of extreme values in finding inflection points
Application of extreme value in finding the maximum value
best value
Definition: (algebraic angle) the maximum and minimum values on the entire interval; (geometric angle) the highest and lowest points of the image
The most valuable method
The difference between maximum value and extreme value: local concept and global concept
Most valuable application
Application of maximum value in finding extreme value
Application of maximum value in finding inflection point
Concave-convex inflection point
Concave-convexity
Definition (Geometry and Algebra)
decision theorem
application
Application of concavity and convexity in finding inflection points
The application of concavity and convexity in finding the optimal value
inflection point
Definition: The dividing point of concavity and convexity
Necessary conditions for determining turning points
Application of inflection point
The application of inflection point in finding the optimal value
Application of inflection point in finding concavity and convexity.
How to judge concavity and inflection points
*curvature
Features: Measure the curvature of the curve for quantitative analysis
Calculation formula
Circle of Curvature and Radius of Curvature
*Applications in economic analysis
Marginal cost, marginal revenue, marginal profit, elasticity of demand