What information does the first derivative tell you?

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What information does the first derivative tell you?

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Answer 1 · 2015-03-08T19:56:42

The first derivative of a function $y=f(x)$ tells you how your function changes when you change $x$ or, if you consider the graph of your function, the inclination of the curve representing it:
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In the example, at $P$ , for each change of 1 unit in $x$ , $y$ changes of 4.

If in $P$ the function had an inclination downwards the derivative would have been negative.
If in $P$ the function had minimum or maximum the derivative would have been zero

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Summarizing, derivative tells you how a variable quatity changes.

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What information does the first derivative tell you?

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