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Home > Study Help and Practice Problems > Math Help > Calculus > Calculus: Applications of the Derivative

Calculus: Applications of the Derivative Help & Problems

Find study help on applications of the derivative for calculus. Use the links below to select the specific area of applications of the derivative you're looking for help with. Each guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn applications of the derivative for calculus.

Study Guides

showing 1 - 10 of 13
  • 1.

    The Derivative as a Rate of Change Help

    Introduction to The Derivative as a Rate of Change If f(t) represents the position of a moving body, or the amount of a changing quantity, at time t , then the derivative f′(t) (equivalently, ( d/dt)f(t)) denotes the rate ...

    Source: McGraw-Hill Professional
  • 2.

    Graphing of Functions Help

    Introduction to Graphing of Functions We know that the value of the derivative of a function f at a point x represents the slope of the tangent line to the graph of f at the point ( x , f(x) ). If that slope is ...

    Source: McGraw-Hill Professional
  • 3.

    Maximum/Minimum Problems Help

    Introduction to Maximum/Minimum Problems One of the great classical applications of the calculus is to determine the maxima and minima of functions. Look at Fig. 3.9. It shows some (local) maxima and (local) minima of the function f .

    Source: McGraw-Hill Professional
  • 4.

    Related Rates Help

    Introduction to Related Rates If a tree is growing in a forest, then both its height and its radius will be increasing. These two growths will depend in turn on (i) the amount of sunlight that hits the tree, (ii) the amount of nutrients in the soil, (iii) the ...

    Source: McGraw-Hill Professional
  • 5.

    Falling Bodies Help

    Introduction to Falling Bodies It is known that, near the surface of the earth, a body falls with acceleration (due to gravity) of about 32 ft/sec 2 . If we let h ( t ) be the height of ...

    Source: McGraw-Hill Professional
  • 6.

    Applications of the Derivative Practice Test

    Review the following concepts if needed: Graphing of Functions Help

    Source: McGraw-Hill Professional
  • 7.

    Rates of Change Study Guide

    Rates of Change It is useful to contemplate slopes in practical situations. For example, suppose the following graph in Figure 8.1 is for y = f(x), a function that gives the price y for various amounts x of cheese. ...

    Source: LearningExpress, LLC
  • 8.

    Differentiate Both Sides of the Equation Study Guide

    Differentiate Both Sides of the Equation Once you have gotten the hang of implicit differentiation, it should not be difficult to take the derivative of both sides with respect to the variable t. This enables us to see how x and y vary ...

    Source: LearningExpress, LLC
  • 9.

    Graphs of Increasing and Decreasing Functions and Asymptotes Study Guide

    Graphs of Increasing and Decreasing Functions and Asymptotes Here is where everything comes together. We know how to find the domain, how to identify asymptotes, and how to plot points. With the help of the sign diagrams from the previous lesson, we shall be able ...

    Source: LearningExpress, LLC
  • 10.

    Rates of Change Practice Questions

    To review these concepts, go to Rates of Change Study Guide. Rates of Change Practice Questions For each of the following four graphs, give the rate that a slope represents. ...

    Source: LearningExpress, LLC
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