Question: Hi, i am trying to find the point of inflexion for the curve y = e^x/(x²-1) and i got a really complex expression for y". I can't seem to solve x⁴-4x³+4x²+4x+3=0 so does that mean there is no point of inflexion?

Hi Sam,

I got the same second derivative as you. I also don't see a solution to
x⁴-4x³+4x²+4x+3 = 0 and I don't know a nice way to show that is has no solutions. I used Mathematica to sketch a graph of y = e^x/(x²-1) for x between -2 and 5 and I got

Graph of y = e^x/(x²-1)

The curve changes concavity at x = -1 and x = 1 but I don't believe there are any inflexion points.

Then I had Mathematica solve x⁴-4x³+4x²+4x+3 = 0 and it gave me four solutions, none of which are real so your conclusion is correct, there are no inflexion points.

Penny