- #1
Hogart
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Homework Statement
We are given the curve y = (1+x)/(1+x^2)
Homework Equations
y' and y''
The Attempt at a Solution
I know the inflection points of y are the local minimum and maximum of y'; this can also be restated as the critical points of y''. My attempt is to find the zero's of y'' and show there are only three critical points that satisfy as being the local extremes of y'. However, I end up getting a huge fifth degree polynomial for y''. This thing is a monster to solve; it does not seem to simplify either.
y'' = (2x^5+6x^4-4x^3+5x^2-8x-3)/(x^4+2x^2+1)^2
Perhaps I can show y'' has three zero's by IVT but there is a second part that requires the actual x values that make those zero's.
Anyone have any other ideas?