**Unformatted text preview: **Starting with one function, √ 625-x 2 , we have derived, by means of some slightly nasty algebra, a new function,-x/ √ 625-x 2 , that gives us important information about the original function. This new function in fact is called the derivative of the original func-tion. If the original is referred to as f or y then the derivative is often written f ± or y ± and pronounced “f prime” or “y prime”, so in this case we might write f ± ( x ) =-x/ √ 625-x 2 . At a particular point, say x = 7, we say that f ± (7) =-7 / 24 or “ f prime of 7 is-7 / 24” or “the derivative of f at 7 is-7 / 24.” To summarize, we compute the derivative of f ( x ) by forming the diﬀerence quotient f ( x + Δ x )-f ( x ) Δ x ,...

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- Fall '07
- JonathanRogawski
- Math, Calculus, Derivative, Rate Of Change