Let `f(x)` be a differentiable function on `[0,8]` such that `f(1)=3, f(2)=1//2, f(3) =4, f(4)=-2, f(5)=6`
`f(6)=1//3, f(7)=-1//4`. Then the minimum no. points of interaction of the curve `y=f^(')(x)` and `y=f^(')(x)(f(x))^(2)` is `K` then `K-5=`

Answer

6

Explanation

`f^(')(x)=f^(')(x)(f(x))^(2)`
Either `f^(')(x)=0` at least 4 roots
`f(x)=1` at least 5 roots
`f(x)=-1` at least 2 roots
at least 11 roots.