6. The Derivative as a Function - Lecture 6 (20150116): The...

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Lecture 6 (20150116): The Derivativeasa FunctionExample 23(Warm-Up: Computing a Derivative).Computef(1), wheref(t) =3t+1.Again, we use the definition of the derivative:limh0f(1 +h)f(1)h=limh032+h32h=limh063(2+h)2(2+h)h=limh03h2h(2 +h)=limh032(2 +h)=34.Suppose that you don’t just want to knowf(1), but alsof(2) andf(3). Because the process usedto find these is exactly the same as that used to computef(1), this could get very tedious very quickly.Indeed, we often just computef(x) forgeneralnumberxonce and for all.Example 24.Computef(x), wheref(x) =3x+1.

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Term
Summer
Professor
Visscher
Tags
Calculus, Derivative, Differential Calculus, lim, Continuous function, Gottfried Leibniz

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