Diffrentiability+Limits

Question

how to solve diffrentiability with standard procedure of f(a+h).

Comments

ans. is B right??

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Yes, B is answer . in answer key 1 and 2 are RhD and LHd but i am getting 1 and 3.

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when you check for differentiability, RHD is 3 for sure. it can not be 2 as f'(x) = 3x for x>1 and 1 for x<= 1

so f'(1) = 3 in case of RHD and 1 in case of LHD. as there is one more method by which you were asking to solve but this one is easy and both give same answer, so you are right @rahul.

Answer 1

blue line is for x-1
pink is for x^3-1


u can see there is a sharp edge at x=1
so not differentiable.