Study Guides
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31.
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 -
Source: McGraw-Hill Professional
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33.
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 -
34.
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 -
35.
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 -
36.
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 -
37.
Applications of the Derivative Practice Test
Review the following concepts if needed: Graphing of Functions Help
Source: McGraw-Hill Professional -
38.
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 -
39.
Area Under a Curve Help
Introduction to Area Under a Curve Consider the curve shown in Fig. 4.1. The curve is the graph of y = f ( x ). We set for ourselves the task of calculating the area A that is (i) under the curve, (ii) above ...
Source: McGraw-Hill Professional -
40.
Signed Area Help
Introduction to Signed Area Without saying so explicitly, we have implicitly assumed in our discussion of area in the last section that our function f is positive, that is its graph lies about the x-axis. But of course many functions do not share ...
Source: McGraw-Hill Professional
