How to get the relative max and min and the inflection point ?
1 Answer
Relative min @ x=0, no relative maxes, inflection point at 4/3
Explanation:
The point of inflection (POI) is defined as points where the second derivative crosses the x-axis.
The second derivative shown has single roots at the square root of 4/3 and is undefined at +/-2.
The root at 4/3 is a single root so this is a POI.
Relative max/mins can be easily found by finding where the first derivative is equal to zero. A positive to negative crossing is a maximum while a negative to positive crossing is a minimum.
The first derivative has a root at 0. To the left, the first derivative is negative and to the right the first derivative is positive so it is a negative to positive crossing. This make it a relative minimum because the function is decreasing and then increasing.
There are no more roots so there is only a rel. min. at 0.
