Function derivatives


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 f'\left( x \right). If the second derivative check-box is selected  you can see that the same relation between the function f\left( x \right) and its first derivative f'\left( x \right) also exist between the first derivative f'\left( x \right) and the second derivative f''\left( x \right) (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 MoroniFebruary 2014