Creating a calculus for dummies book. Just a few definition questions

You don't have to help with all of it. Any help at all would be appreciated! Thank you!
(I have already done the rest of the project, these are just the ones I'm stuck on)

-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?
-Information on min/max/POI

Antiderivatives (indefinite integrals)
-What is it?
-What is the power rule for anti derivatives
Then I need 2 examples.

-Applications- 2 application problems (1 physics, 1 other)

Derivative: Lim h -> 0 [f(x + h) - f(x)] / [h]

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

Here's many, many examples of the rules:

http://en.wikipedia.org/wiki/Differentia…

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)

The anti-derivative of a function is the function whose derivative equals the original function.

∫ x^n dx = [1/(n + 1)]x^(n + 1) + C for n ≠ -1
∫ x^(-1) dx = ln|x| + C for n = -1

Here's many, many examples:

http://en.wikipedia.org/wiki/Lists_of_in…

Physics application:

Work = ∫ F dx (limits from x1 to x2)

Area between function and x axis between x = a and x = b:

∫ f(x) dx (limits from a to b)

Done!