Improved Second Derivative Test for Relative Extrema
International Journal of Mathematical Education in Science and Technology
In this note, a modified Second Derivative Test is introduced for the relative extrema of a single variable function. This improved test overcomes the difficulty of the second derivative vanishing at the critical point, while in contrast the traditional test fails for this case. A proof for this improved Second Derivative Test is presented, followed by an example.
"Improved Second Derivative Test for Relative Extrema."
International Journal of Mathematical Education in Science and Technology, 38 (8): 1121-1123.
doi: 10.1080/00207390701453504 source: https://www.tandfonline.com/doi/full/10.1080/00207390701453504