Q. 94.5( 2 Votes )

Show that the function

F(x) =

Is continuous but not differentiable at x = 1.

Answer :

F(x) =


For continuity at x = 1


F(1) = - (2(1) - 3) = 1


LHL =


=


=


= sin


= 1


RHL =


=


=


= - 1( - 1)


= 1


LHL = RHL = f(1)


So, f(x) is continuous at x = 1


For differentiability at x = 1


(LHD at x = 1) =


=


=


=


=


= 0


(RHD at x = 1) =


=


=


=


=


= - 2


(LHD at x = 1)(RHD at x = 1)


Hence, f(x) is continuous but not differentiable at x = 1.


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