What information does the first derivative tell you?

1 Answer
Gió
Mar 8, 2015

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:
enter image source here
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

enter image source here

Summarizing, derivative tells you how a variable quatity changes.

Hope it helps

Related questions
See all questions in Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)
Impact of this question
8547 views around the world
You can reuse this answer
Creative Commons License