CGPET 2012 Solved Paper

Given, ‌‌f(x)=(x−1)2∕3
It is clear that, f(x) is continuous everywhere.
On differentiating w.r.t. ' x,' we get
f′(x)=‌

2

3(x−1)1∕3

Here, at x=1,f′(x) is not defined, so it is not differentiable at x=1.
So, option (a), (b) and (c) are not correct.
Hence, option (d) is correct.