Applications of derivatives
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This document discusses various applications of derivatives including instantaneous velocity, acceleration and position as well as average acceleration and velocity. It also covers concepts like change over time, velocity, and position as well as local maxima and minima, optimization problems involving minimizing and maximizing area, perimeter and volume, and absolute minimums and maximums as the high and low points on a graph.
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Calculus Final Review Joshua Conyers
1) Derivatives relate the rates of change of position, velocity, and acceleration. Velocity is the derivative of position and measures rate of change of displacement. Acceleration is the derivative of velocity and measures the rate of change of velocity.
2) The Mean Value Theorem states that for a continuous function over an interval, there exists at least one point where the slope of the tangent line equals the slope of the secant line between the endpoints.
3) A function's derivatives provide information about the behavior of the original function. The first derivative relates to slope and critical points where the function is increasing/decreasing. The second derivative indicates points of inflection where the concavity changes.
Application of derivatives
This document discusses key concepts in calculus including derivatives, position, velocity, and acceleration and how they relate to graphs. It covers finding absolute and local maxima and minima, determining if a function is increasing or decreasing based on the first derivative, and using the second derivative to determine concavity.
3.1 higher derivatives
The document discusses higher order derivatives. It defines the nth derivative of a function f(x) as f(n)(x). The first example finds the first five derivatives of f(x)=2x^4 - x^3 - 2. The second example finds the first three derivatives of f(x)=-x^2/3. The third example finds the first four derivatives of f(x)=ln(x) and discusses how derivatives of rational functions become more complicated with higher orders. It also provides examples of finding derivatives of other functions like sin(x).
Application of partial derivatives with two variables
Application of Partial Derivatives with Two Variables
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Application of derivatives
The document discusses several key concepts regarding derivatives:
(1) It explains how to use the derivative to determine if a function is increasing, decreasing, or neither on an interval using the signs of the derivative.
(2) It provides theorems and rules for finding local extrema (maxima and minima) of functions using the first and second derivative tests.
(3) It also discusses absolute extrema, monotonic functions, and the Rolle's Theorem and Mean Value Theorem which relate the derivative of a function to values of the function.
The Application of Derivatives
This document discusses several topics related to calculus including:
1) Derivatives of position, velocity, and acceleration and how they relate to each other.
2) An example problem calculating velocity from a position function.
3) The Mean Value Theorem and how to apply it to find critical points of a function.
4) How the first and second derivatives of a function relate to critical points, maxima, minima, and points of inflection or concavity.
5) Related rates problems and how to set them up using derivatives and relationships between variables.
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Calculus Final Review Joshua Conyers
1) Derivatives relate the rates of change of position, velocity, and acceleration. Velocity is the derivative of position and measures rate of change of displacement. Acceleration is the derivative of velocity and measures the rate of change of velocity.
2) The Mean Value Theorem states that for a continuous function over an interval, there exists at least one point where the slope of the tangent line equals the slope of the secant line between the endpoints.
3) A function's derivatives provide information about the behavior of the original function. The first derivative relates to slope and critical points where the function is increasing/decreasing. The second derivative indicates points of inflection where the concavity changes.
Application of derivatives
This document discusses key concepts in calculus including derivatives, position, velocity, and acceleration and how they relate to graphs. It covers finding absolute and local maxima and minima, determining if a function is increasing or decreasing based on the first derivative, and using the second derivative to determine concavity.
3.1 higher derivatives
The document discusses higher order derivatives. It defines the nth derivative of a function f(x) as f(n)(x). The first example finds the first five derivatives of f(x)=2x^4 - x^3 - 2. The second example finds the first three derivatives of f(x)=-x^2/3. The third example finds the first four derivatives of f(x)=ln(x) and discusses how derivatives of rational functions become more complicated with higher orders. It also provides examples of finding derivatives of other functions like sin(x).
Application of partial derivatives with two variables
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Maxima And Minima Values.
Maximum And Minimum Values.
Tangent and Normal.
Error And Approximation.
Application of derivatives
The document discusses several key concepts regarding derivatives:
(1) It explains how to use the derivative to determine if a function is increasing, decreasing, or neither on an interval using the signs of the derivative.
(2) It provides theorems and rules for finding local extrema (maxima and minima) of functions using the first and second derivative tests.
(3) It also discusses absolute extrema, monotonic functions, and the Rolle's Theorem and Mean Value Theorem which relate the derivative of a function to values of the function.
The Application of Derivatives
This document discusses several topics related to calculus including:
1) Derivatives of position, velocity, and acceleration and how they relate to each other.
2) An example problem calculating velocity from a position function.
3) The Mean Value Theorem and how to apply it to find critical points of a function.
4) How the first and second derivatives of a function relate to critical points, maxima, minima, and points of inflection or concavity.
5) Related rates problems and how to set them up using derivatives and relationships between variables.
First order linear differential equation
1. A differential equation relates an unknown function and its derivatives, and can be ordinary (involving one variable) or partial (involving partial derivatives).
2. Linear differential equations have dependent variables and derivatives that are of degree one, and coefficients that do not depend on the dependent variable.
3. Common methods for solving first-order linear differential equations include separation of variables, homogeneous equations, and exact equations.
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This document provides the derivatives of various functions. It begins with basic derivatives like sin(x), cos(x), and e^x. It then covers the derivatives that follow rules like the quotient rule, product rule, chain rule, and derivatives of inverse functions. The responses provide concise answers to the derivative questions in 1-3 sentences each.
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Applications of derivatives
- 1. Applications of Derivatives Jessica Catanese
- 2. INSTANTANEOUS Velocity Acceleration Position
- 3. DERIVATIVE
- 5. Change in… Time Velocity Position
- 8. OPTIMIZATION
- 9. Minimizing & Maximizing AreaPerimeterVolume
- 11. High and low points on a graph