+91-8076753736 support@wiredfaculty.com

Sponsor Area

Continuity And Differentiability

Question

Wired Faculty App

Prove that the greatest integer function [x] is not differentiable at x = 1.

Solution

Let space straight f left parenthesis straight x right parenthesis equals left square bracket straight x right square bracket Lt with straight x rightwards arrow 1 to the power of minus below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow 1 to the power of minus below left square bracket straight x right square bracket space space space space space space space space space left square bracket Put space straight x equals 1 minus straight h comma space straight h greater than 0 space so space that space straight h rightwards arrow 0 space as space straight x rightwards arrow 1 to the power of minus right square bracket space space space space space space space space space space space space equals Lt with straight h rightwards arrow 0 below left square bracket 1 minus straight h right square bracket equals Lt with straight h rightwards arrow 0 below left parenthesis 0 right parenthesis equals 0 space space space space Lt with straight x rightwards arrow 1 to the power of plus below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow 1 to the power of plus below left square bracket straight x right square bracket space space space space space left square bracket Put space straight x equals 1 plus straight h comma space straight h greater than 0 space so space that space straight h rightwards arrow 0 space as space straight x rightwards arrow 1 to the power of plus right square bracket space space space space space space space space space space space space space space space space equals Lt with straight h rightwards arrow 0 below left square bracket 1 plus straight h right square bracket equals Lt with straight h rightwards arrow 0 below left parenthesis 1 right parenthesis equals 1 therefore space Lt with straight x rightwards arrow 1 to the power of minus below straight f left parenthesis straight x right parenthesis not equal to Lt with straight x rightwards arrow 1 to the power of plus below straight f left parenthesis straight x right parenthesis rightwards double arrow space straight f space is space not space continous space at space straight x equals 1 space space space space space rightwards double arrow straight f space is space not space differentiable space at space straight x equals 1

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation