How derivatives are helpful to find the behavior of graph of function'?

Question

How derivatives are helpful to find the behavior of graph of function?

Answer 1

You can use the 1st derivative to find maximum and minimum points (find the 1st derivative, and set it to zero).
You can use the second derivative to find where the graph curves upward or downward (if the 2nd derivative is positive, the graph curves upward, if it is negative the graph curves downward, if the 2nd derivative is 0 the graph is linear).

Answer 2

Derviatives show you how the graph slopes up or down.

So for example if the derivative is zero, the line is flat - that is, it has no slope - that is, it's parallel to the x-axis.

If the derivative at some point is very positive, that's a very big slope upwards.
If the derivative at some point is very negative, that's a very big slope downwards.

Hope this helps!

Answer 3

First derivatives tell you when the function stops growning, like where there might be a max or min.

Second derivatives tell you where the function changes from growing faster to growing slower. I.E. When it changes from concave up to concave down.