Question

What information does the first derivative tell you?

Answer 1

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:

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

Summarizing, derivative tells you how a variable quatity changes.

Hope it helps