Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
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

  1. A1
  2. B0
  3. C4 / 5
  4. 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

Practice Differentiation on Quantrex Academy →

More from Differentiation

The domain of the derivative of the function f(x)= x 1+|x| is 2025If x= 2^ cosec ⁻¹ t and y= 2^ ⁻¹ t ,|t| 1 then d y d x = 2025If (a+ 2 b x)(a- 2 b y)=a^2-b^2 where a>b>0 , then at ( 4 , 4 ) , dy dx = 2025If x y - y x =0 , then d y d x = 2025If y = ( _ x x )^ x , then dy dx = 2025If f(x)=x^ Sec ⁻¹ x , then f^ (2)= 2025If y= x^4 3 x-5 (x^2-3 )(2 x-3) , then ( d y d x )_ x=2 = 2025If x^2+y^2+ y=4 , then the value of d^2 y d x^2 at x=-2 is 2025 Full Differentiation list All AP EAMCET PYQs