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 19:16:54One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
Project management is the process of applying specialized knowledge, skills, tools, and methods to project activities so that the project can achieve or exceed the set needs and expectations within the constraints of limited resources. This diagram provides a comprehensive overview of the 8 components of the project management process and can be used as a generic template for direct application.
One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
Project management is the process of applying specialized knowledge, skills, tools, and methods to project activities so that the project can achieve or exceed the set needs and expectations within the constraints of limited resources. This diagram provides a comprehensive overview of the 8 components of the project management process and can be used as a generic template for direct application.
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