` `

```
```

` `

*How to run a CDF Player simulation
download Functionderivatives.cdf
download Functionderivatives.nb (Mathematica notebook)*

**Notes**:

Drag the blue marker along the *x* axis to change the function point for which the tangent line and its slope are calculated, The slope of the tangent line is the *y*-value of the function’s first derivative . If the second derivative check-box is selected you can see that the same relation between the function and its first derivative also exist between the first derivative and the second derivative (see it yourself…).

*Understanding*

Ask yourself:

*when the first derivative is positive the function is…**when the function is decreasing the first derivative is…**when the first derivative crosses the x axis the function has…**when the function crosses the x axis the first derivative is…**when the function has a local maximum (or minimum) the first derivative…**when the first derivative has a local maximum (or minimum) the second derivative…**when the function is concave upwards (smiling) its second derivative is…**when the function is concave downwards (sad) its second derivative is…**when the second derivative is zero the first derivative … and the function…**when the second derivative is positive (negative) the first derivative …. and the function….*

[*answers*]

See also: “*A poly function and its derivative*“

Credits:

Derivative as a Function by Jim Brandt

Derivatives: A Look at Graphs by Abby Brown

from the Wolfram Demonstrations Project

Author: **Luca Moroni** – *February 2014*