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1. openstax.org › books › calculus-volume-13.4 Derivatives as Rates of Change - Calculus Volume 1 - OpenStax

   openstax.org › books › calculus-volume-1

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   In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.

   • 4.4 The Mean Value Theorem

     Corollaries of the Mean Value Theorem. Let’s now look at...

   • 3.7 Derivatives of Inverse Functions

     Find the rate of change of the angle of elevation after...

   • 4.5 Derivatives and The Shape of a Graph

     Using the First Derivative Test. Consider a function f f...

   • 4.7 Applied Optimization Problems

     Write a formula for the quantity to be maximized or...

   • 6.9 Calculus of The Hyperbolic Functions

     Learning Objectives. 6.9.1 Apply the formulas for...

   • 1.2 Basic Classes of Functions

     One of the distinguishing features of a line is its slope....

   • 3.5 Derivatives of Trigonometric Functions

     Learning Objectives. 3.5.1 Find the derivatives of the sine...

   • 4.2 Linear Approximations and Differentials

     Analysis. Using a calculator, the value of 9.1 9.1 to four...

2. abel.math.harvard.edu › ~knill › teachingUnit 7: Rate of Change - Harvard University

   abel.math.harvard.edu › ~knill › teaching

   INTRODUCTION TO CALCULUS. MATH 1A. Unit 7: Rate of Change. Lecture. 7.1. Given a function f and a constant h > 0, we can look at the new function. f(x + h) f(x) Df(x) = : h. It is the average rate of change of the function with step size h. When changing x to x + h and then f(x) changes to f(x + h).

3. people.math.harvard.edu › ~knill › teachingn Lecture 7: Rate of change - Harvard University

   people.math.harvard.edu › ~knill › teaching

   Lecture 7: Rate of change. A function f leads to a new function. f(x + h) − f(x) Df(x) = . h. It is the rate of change of the function with step size h. When changing. response change f(x) to f(x + h). In this lecture, we take the limit h important formulas dxxn d = nxn−1, d d dx exp(x) = exp(x), dx sin(x) = cos(x), to x + h → and get.

4. people.math.harvard.edu › ~knill › teachingLecture 7: Rate of change - Harvard University

   people.math.harvard.edu › ~knill › teaching

   Lecture 7: Rate of change. Given a function f and h > 0, we can look at the new function. f(x + h) f(x) Df(x) = : h. It is the rate of change of the function with step size h. When changing x to x + h and then f(x) changes to f(x + h). The quotient Df(x) is "rise over run". In this lecture, we take the.

5. www3.nd.edu › ~apilking › Math10550Lecture 6 : Derivatives and Rates of Change - University of Notre...

   www3.nd.edu › ~apilking › Math10550

   The derivative, f0(a) is the instantaneous rate of change of y= f(x) with respect to xwhen x= a. When the instantaneous rate of change is large at x 1, the y-vlaues on the curve are changing rapidly and the tangent has a large slope. When the instantaneous rate of change ssmall at x 1, the y-vlaues on the

6. emedia.rmit.edu.au › learninglab › sitesApplications of Differentiation DN1.10: RATES OF CHANGE - RMIT

   emedia.rmit.edu.au › learninglab › sites

   Find a formula for the instantaneous rate of change of energy with respect to velocity for a body with a mass of 10kg.

7. lor.usq.edu.au › 1 › C6_DifferentiationDescribingChange_Jan14Module Describing change – an introduction to differential...

   lor.usq.edu.au › 1 › C6_DifferentiationDescribingChange_Jan14

   use graphs and algebra to describe the rate of change of a function. determine the instantaneous rate of change of a function. apply the power, sum and difference rules to find the derivative of certain polynomial functions. apply calculus to velocity and acceleration and other real life problems.