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Investigate monotonicity: multi-parameter function & complicated region?

jakub zbec

Posted 8 years ago

I just don't know how to do it all. I got is in the attachment file. I know i need to use derivative but this function is just to massive for me. RegionPlot3D[0<=1/4(1?a?b?c)&& 1/4(1?a?b?c)<=1&& 0<=1/4(1+a+b?c)&& 1/4(1+a+b?c)<=1&& 0<=1/4(1+a?b+c)&& 1/4(1+a?b+c)<=1&& 0<=1/4(1?a+b+c)&& 1/4(1?a+b+c)<=1&& a^2<b^2&&b^2<c^2,{a,-1,1},{b,-1,1},{c,-1,1}, AxesLabel->{"a","b","c"}, PlotPoints->50] f[x_] := (Sqrt[1 - a + (b + c) (c + b x - c x) - Sqrt[(b + 2 c - a c)^2 - (b^2 - c^2) (-3 + 4 a - a^2 + b^2 - c^2) x + (b^2 - c^2)^2 x^2]] + Sqrt[1 - a + (b + c) (c + b x - c x) + Sqrt[(b + 2 c - a c)^2 - (b^2 - c^2) (-3 + 4 a - a^2 + b^2 - c^2) x + (b^2 - c^2)^2 x^2]] + Sqrt[1 + a - (b - c) (c - b x - c x) - Sqrt[(b - 2 c - a c)^2 - (b^2 - c^2) (-3 - 4 a - a^2 + b^2 - c^2) x + (b^2 - c^2)^2 x^2]] + Sqrt[1 + a - (b - c) (c - b x - c x) + Sqrt[(b - 2 c - a c)^2 - (b^2 - c^2) (-3 - 4 a - a^2 + b^2 - c^2) x + (b^2 - c^2)^2 x^2]])^2; Attachments:

I just don't know how to do it all. I got is in the attachment file. I know i need to use derivative but this function is just to massive for me.

RegionPlot3D[0<=1/4(1?a?b?c)&&
1/4(1?a?b?c)<=1&&
0<=1/4(1+a+b?c)&&
1/4(1+a+b?c)<=1&&
0<=1/4(1+a?b+c)&&
1/4(1+a?b+c)<=1&&
0<=1/4(1?a+b+c)&&
1/4(1?a+b+c)<=1&&
a^2<b^2&&b^2<c^2,{a,-1,1},{b,-1,1},{c,-1,1}, 
AxesLabel->{"a","b","c"}, PlotPoints->50]

enter image description here

f[x_] := (Sqrt[1 - a + (b + c) (c + b x - c x) - 
       Sqrt[(b + 2 c - a c)^2 - (b^2 - c^2) (-3 + 4 a - a^2 + b^2 - c^2) x + (b^2 - c^2)^2 x^2]] + 
     Sqrt[1 - a + (b + c) (c + b x - c x) + 
       Sqrt[(b + 2 c - a c)^2 - (b^2 - c^2) (-3 + 4 a - a^2 + b^2 - c^2) x + (b^2 - c^2)^2 x^2]] + 
     Sqrt[1 + a - (b - c) (c - b x - c x) - 
       Sqrt[(b - 2 c - a c)^2 - (b^2 - c^2) (-3 - 4 a - a^2 + b^2 - c^2) x + (b^2 - c^2)^2 x^2]] + 
     Sqrt[1 + a - (b - c) (c - b x - c x) + 
       Sqrt[(b - 2 c - a c)^2 - (b^2 - c^2) (-3 - 4 a - a^2 + b^2 - c^2) x + (b^2 - c^2)^2 x^2]])^2;