# math

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I have the same project as Jill down there...

-What is the definition of a derivative?
-What does the derivative of a function tell you (in english) ?
Then I need an example of the power rule, quotient rule, and chain rule.

-What information does the FIRST derivative tell you about a function?
-What information does the SECOND derivative tell you about a function?

• math -

The derivative of a function tells you the instantaneous rate of change of the function at every point.

The first derivative tells you the slopes of the function
The second derivative tells you the slope of the slope (aka. the concavity)

First derivative = 0 or undefined => Critical point
Second derivative at critical point positive = > minimum
Second derivative at critical point negative = > maximum
Second derivative at critical point zero = > inflection point (probably)

I google type:
wikipedia Differentiation rules

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