Study Guides
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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.
Implicit Differentiation Study Guide
Implicit Differentiation A common complaint about the Chain Rule is "I don't know where to stop!" For example, why do we use the Chain Rule for f(x) = sin(x3) to get f'(x) = ...
Source: LearningExpress, LLC -
9.
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 -
10.
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
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