Let `f(x)=a/x+x^2dot` If it has a maximum at `x=-3,` then find the value of `adot`

Explanation

`A=sinx+cosx`

`A^2=sin^2x+cos^2x+2sinxcosx`

`A^2=(A^2/2-1)`

`sin^4x+cos^4x=(sin^2x)^2+(cos^2x)^2`

`=(sin^2x+cos^2x)^2-2sin^2xcos^2x`

`=1-2(sinxcosx)^2`

`=1-2*(A^2-1)^2/4`

`=(2-(A^2-1)^2)/2`.