In many books a shortcut trick for checking differnetiabiltiy of a fuction is given by first differentiate LHS and RhS and check if both the slope are coming same, provided the function is continous. However in many question this method will not work like in this question
'f(x)= (x-1)^2* sin (1/x-1) - modx for x not equal to 0
and f(x)=1 for x=1
check the differntiability of the function . In this question the two points will be 0 and 1 . Observe that on applying this trick on lhs at x=1 the slope is not coming what is calculated by f(a+h)-f(a)/h .So my question is when can we apply this method and when we cant
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3 Answers
1357we can rely on that rule only if f'(x) is continuous.
If f'(x) is not continuous at some points, then check differentiability at those points.