Question : canonical equations where minima or maxima have second derivative = 0

Hi

I was wondering if you knew of any common equations where you can't tell from looking at the second derivative whether a turning point is a minima or maxima because the second derivative = 0. Is y = x^4 an example because it has a turning point at 0 and the second derivative is 0 at x=0? You can however tell y = x^4 is minima from the first derivative test of looking at signs of nearby values. Are there any other common examples?

thanks

Answer : canonical equations where minima or maxima have second derivative = 0

"Doesn't y = x^3 have a point of inflection?" yes that is it. I see now that you did not want it.
You have given the best example y = x^4
you can try
y=x^n where n can be any even integer
(the max or min gets flatter as n imcreases