AboutAbe Mantell Expertise Hello,
I am a college professor of mathematics and regularly teach all levels
from elementary mathematics through differential equations, and would
be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
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.
