consider `f(X) =(1)/(1+|x|)+(1)/(1+|x-1|)` Let `x_(1)` and `x_(2)` be point wher f(x) attains local minmum and global maximum respectively .If `k=f(x_(1))+f(x_(2))` then 6k-9=________.

Answer

8

Explanation

`f(X)=(1)/(1+|x|)+(1)/(1+|x-1|)`
clearly f(X) is non differeentiable at x =0,1
Also `f(1//2+x)=f(1//2-x)`
Hence graph of f(x) is symmetrical about line x=`1//2` where derivation is zero
Local minimum =`f(1/2)=4/3`
Global maximum `=f(x)=f(1)=3/2`
`terefore k=4/3+3/2=17/6`