Study Guides
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11.
Continuity Help
Introduction to Continuity Let f be a function whose domain contains the interval (a, b). Assume that c is a point of (a, b). We say that the function f is continuous at c if
Source: McGraw-Hill Professional -
12.
The Derivative Help
Introduction to The Derivative Suppose that f is a function whose domain contains the interval (a , b). Let c be a point of (a , b). If the limit
Source: McGraw-Hill Professional -
13.
Rules for Calculating Derivatives Help
Introduction to Rules for Calculating Derivatives Calculus is a powerful tool, for much of the physical world that we wish to analyze is best understood in terms of rates of change. It becomes even more powerful when we can find some simple rules that enable us to ...
Source: McGraw-Hill Professional -
Source: McGraw-Hill Professional
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15.
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 -
16.
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 -
17.
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 -
18.
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 -
19.
Applications of the Derivative Practice Test
Review the following concepts if needed: Graphing of Functions Help
Source: McGraw-Hill Professional -
20.
Antiderivatives Help
Introduction to Antiderivatives Many processes, both in mathematics and in nature, involve addition. You are familiar with the discrete process of addition, in which you add finitely many numbers to obtain a sum or aggregate. But there are ...
Source: McGraw-Hill Professional
