Let `f(x)=sqrt(x-1)+sqrt(x+24-10sqrt(x-1)), 1ltxlt26` be real valued function, then `f'(x)` for `1ltxlt26` is

Options

A. 0
B. `(1)/(sqrt(x-1))`
C. `2sqrt(x-1)`
D. none of these

Answer

A

Explanation

We have,
`f(x)=sqrt(x-1)+sqrt((x-1)+25-10sqrt(x-1))`
`implies" "f(x)=sqrt(x-1)+sqrt("("sqrt(x-1)-5")"^(2))`
`implies" "f(x)=sqrt(x-1)+|sqrt(x-1)-5|`
`implies" "f(x)=sqrt(x-1)-"("sqrt(x-1)-5")"" "[{:(becausesqrt(x-1)-5lt0),(" for "1ltxlt26):}]`
`:." "f'(x)=0" for all "x in(1,26).`