AP EAMCET202315 May 2023Evening ShiftMathematicsDifferentiationActual
If f(x)=|x-5|+|x+5|+|x-4|+|x+4| , then f^ (1)-f^ (-6) f^ (-1)+f^ (6) =
Options
- A1
- B0
- C4 / 5
- D3 / 2
Correct answer
A. 1
Step-by-step solution
Given the function aligned & f(x)=|x-5|+|x+5|+|x-4|+|x+4| & = array cc -4 x & x -5 -2 x+10 & -5 < x -4 18 & -4 < x 4 2 x+10 & 4 < x 5 4 x & 5 < x array . aligned Now f^ (x)= array cc -4 & x -5 -2 & -5 < x -4 0 & -4 < x 4 2 & 4 < x 5 4 & 5 < x array . So, f^ (1)-f^ (-6) f^ (-1)+f^ (6) = 0-(-4) 0+4 = 4 4 =1