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

Explanation

Finding the value of the determinant


`f(x)=(x+a^2)(x^2+xc^2+xb^2+b^2c^2−b^2c^2)−ab(abx+abc^2−abc^2)+ac(ab^2c−ab^2c−acx)`

`f(x)=(x+a^2)(x^2+x(b^2+c^2))−a^2b^2x−a^2c^2x`

`f(x)=x^3+x^2(a^2+b^2+c^2)`

Hence the function is an increasing function