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in trying to sketch the curve of y=(2-x^2)/(1+x^4)
y'=(-2x-8x^3+2x^5)/(1+x^4)^2
y''=[ (1+x^4)^2(-2-24x^2+10x^4)-(-2x-8x^3+2x^5)8x^3(1+x^4) ] / (1+x^4)^4
=[ -2(1+x^4)(1+12x^2-5x^4)+16x^4(1+4x^2-x^4) ] /(1+x^4)^3
dead end
y'=(-2x-8x^3+2x^5)/(1+x^4)^2
y''=[ (1+x^4)^2(-2-24x^2+10x^4)-(-2x-8x^3+2x^5)8x^3(1+x^4) ] / (1+x^4)^4
=[ -2(1+x^4)(1+12x^2-5x^4)+16x^4(1+4x^2-x^4) ] /(1+x^4)^3
dead end