- #1

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- Thread starter Aichuk
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- #1

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- #2

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What *is *the derivative at 8, conceptually?

- #3

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1/12

- #4

Mark44

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Look at the graph of ##y = x^{1/3}##. The derivative, dy/dx, gives the slope of the tangent line to this curve. The formula you show gives you the y values on the tangent line, which is close to, but slightly different from the y values on the curve.

Since the tangent line at (8, 2) lies above the curve ##y = x^{1/3}## , the approximate values will be a little larger than the values on the curve.

- #5

Mark44

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Number Nine said:Whatisthe derivative at 8, conceptually?

The value of the derivative isn't what Number Nine was asking. He was asking about the1/12

- #6

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- #7

Mark44

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Most calculus texts contain formulas, but they usually contain explanatory text as well. Are you saying that your textbook doesn't have explanations to go with the formulas? Sometimes students focus on the formulas and ignore the surrounding text.

- #8

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For example it is really hard to determine ##\sin(0.1\,\rm rad)## without using a calculator. But since the tangent line has a simple form, namely ##y=mx+b##, one can easily exploit the fact that the tangent line resembles the curve of ##\sin x## near ##0## since ##0.1## is approximately zero to find a rough estimate for ##\sin(0.1\,\rm rad)##.

- #9

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Most calculus texts contain formulas, but they usually contain explanatory text as well. Are you saying that your textbook doesn't have explanations to go with the formulas? Sometimes students focus on the formulas and ignore the surrounding text.

My textbook contains examples of HOW to use, but not WHY

- #10

Mark44

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Assuming each section of your textbook ends with a set of problems, maybe these problems are the WHY the formulas are used.My textbook contains examples of HOW to use, but not WHY

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