Expert: Abe Mantell - 7/20/2009

Question
Question:

Function f(x) = x^4-3x^2
1st Der     f ‘ (x) = 4x^3-6x
2nd Der    f ” (x) =12x^2-6
3rd Der    f ’”(x) = 24x
4th Der    f ””(x) = 24

Questions:
1). When the 3rd derivative intersects (POI) the 2nd Derivative at x = -0.22474, what is happening?

2).  Where is maxiumum “jerk” (3rd derivative) occurring on the position curve f(x)=x^4-3x^2?


Answer
1. What is happening to f(x) or f''(x)???

2. You want to maximize f'''(x)?  So, take the derivative of f'''(x),
.  which is f''''(x)=24, but f''''=24 and is never zero.  So the
.  maximum and minimum values will occur at the endpoints of an
.  interval.  If we are looking at the entire domain, then there is
.  no maximum.

Abe