(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'd always used the 2nd derivative test for the nature of stationary points. But I came across this equation in one of my exercises, for which the test doesn't seem to work at all.

Find the stationary points of: y=(x^2-1)^{4}, stating the nature of each.

2. Relevant equations

Using normal calc: the stationary points are at (-1,0), (0,1) and (1,0)

3. The attempt at a solution

Although the double derivative works for when x=0, (local max)

When I sub in the values x=1 or x=-1, the value I end up with is 0: suggesting that these points are stationary points of inflection, when they are not (they're actually local minima).

Please help. :)

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Exception to second derivative test? (Or am I doing something wrong?)

**Physics Forums | Science Articles, Homework Help, Discussion**