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CBSE Class 12-science Answered

 
Q-1  IS   ROLL'S   THEOREM  is  applicable on  x+1/x  in interval  [-1 1] ?  please  give  reason ?  
 
 
Q-2   Is  it necessary  that  mean  value theorem   is also verified  on a function if roll's theorem is applicable on it 
Asked by Aakash | 25 Jan, 2016, 04:46: PM
answered-by-expert Expert Answer
begin mathsize 11px style For space rolle apostrophe straight s space theorem space to space be space applicable space in space straight a space given space interval space left square bracket straight a comma straight b right square bracket space of space straight a space function space straight f left parenthesis straight x right parenthesis comma 1. space straight f left parenthesis straight a right parenthesis equals straight f left parenthesis straight b right parenthesis 2. space straight f left parenthesis straight x right parenthesis space is space continuous space in space left square bracket straight a comma straight b right square bracket 3. space straight f left parenthesis straight x right parenthesis space is space differentiable space in space left parenthesis straight a comma space straight b right parenthesis Here space straight x plus 1 over straight x space in space the space interval space left square bracket negative 1 comma space 1 right square bracket space does space not space satisfy space there space conditions. straight f left parenthesis 1 right parenthesis equals 2 comma space straight f left parenthesis negative 1 right parenthesis equals negative 2. space They space are space not space equal. space Also comma space straight f left parenthesis straight x right parenthesis space is space not space defined space for space straight x equals 0. space Hence comma space the space function space is space discontinuous space and space non minus differentiable space at space straight x equals 0. Hence comma space Rolle apostrophe straight s space theorem space is space not space applicable space for space the space function space in space the space given space interval. straight P. straight S. space Please space ask space straight a space single space question space in space straight a space single space post space end style
Answered by satyajit samal | 25 Jan, 2016, 07:18: PM

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