# What information does the first derivative tell you?

Mar 8, 2015

The first derivative of a function $y = f \left(x\right)$ 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