Mathematics: Derivatives Derivatives: An Explanation Term Paper

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The origin is defined as the point (0, 0), or "X is zero and Y is zero."

If one plots two points on a graph and draws a line between them, then imagines an object following the line starting on the left and going to the right, one can see that the location of the object, which is also a point, is changing as it follows the line. Namely, the X values are increasing (because the object is going from the left to the right), and the Y values are doing whatever the line is doing. In the example shown, the Y values are increasing, because the numbers are getting higher and higher -- that is, according to the proper vocabulary, they are getting more and more positive.

In this case, a derivate is the answer to the question, "how fast are those values changing?" or, "for every time the X value goes up by one, how much does the Y value change?" One may see that the line connecting the two points is slanted, and looks like the side of a mountain slope.

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The "steepness" of the line is called the "slope," and the derivative is the slope at one specific point on the line: that is, the instantaneous slope. The derivate, then is the answer to the question: "what is the instantaneous slope at a given point on the line?"

Derivatives are a useful tool in calculus because they allow one to study how things change. Sometimes things will change based on time, and sometimes they will change based on some physical condition, like altitude or pressure. Derivates can easily be applied to all of these situations and….....

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