
Calculus 1
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Calculus answers two main questions about functions. (1) How steep is a function at a point? (2) What is the area under the graph over some region?
The first question is answered using the derivative and to answer the second question we use the integral.
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Derivative
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When x increases by h, the ratio of a change in F(x) to the change in x that caused it, is equal to [ F(x+h)  F(x) ] / h. As h approaches 0, the limit of the ratio becomes a value. A function that maps x to this limit is called the derivative of F(x).
http://qindex.info/d.php?c=5028#5197


03 Rates of Change
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Galileo had already discovered some years prior that the distance traveled by a falling object is represented by a function of time. Newton wondered how one could calculate the velocity of the object at any particular instance during the fall.
http://qindex.info/d.php?c=5028#5034

