Derivatives Part II
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"In Chapter 2, we learned how to find the slope of a tangent to a curve as the limit of the slopes of secant lines. In Section 2.4, we derived a formula for the slope of the tangent at an arbitary point (a, 1/a) on the graph of the function f(x) = 1/x and sowed that it was -1/a^2.
This seemingly unimportant result is more powerful than it might appear at first glance, as it gives us a simple way to calculate the instantaneous rate of change of f The study of rates of change of functions is called differential calculus, and formula -1/a^2 was our first look at a derivative. The derivative was the 17th-century breakthrough that enabled mathematicians to unlock the secrets of planetary motion and gravitational attraction-- of objects changing position over time. " --Calculus: Graphical, Numerical, Algebraic AP Edition |