If `a , b , c` are real numbers, then find the intervals in which `f(x)=|[x+a^2,ab,ac],[ab,x+b^2,bc],[ac,bc,x+c^2]|` is increasing or decreasing.

Explanation

Given,

`|[x+a^2,ab,ac],[ab,x+b^2,bc],[ac,bc,x+c^2]|`

`=1/(abc)|[a(x+a^2),a^2b,a^2c],[ab^2,b(x+b^2),b^2c],[ac^2,bc^2,c(x+c^2)]|`

`=(abc)/(abc)|[(x+a^2),a^2,a^2],[b^2,(x+b^2),b^2],[c^2,c^2,(x+c^2)]|`


`=[(x+a^2),a^2,a^2],[b^2,(x+b^2),b^2],[c^2,c^2,(x+c^2)]`


`=|[(x+a^2+b^2+c^2),(x+a^2+b^2+c^2),(x+a^2+b^2+c^2)],[b^2,(x+b^2),b^2],[c^2,c^2,(x+c^2)]|`

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