Let f(x) be a real valued function. Then its
Left Hand Derivative (L.H.D.): `Lf'(a)=lim_(h to 0) (f(a-h)-f(a))/-h`
Right Hand Derivative (R.H.D.): `Rf'(a)=lim_(h to 0) (f(a+h)-f(a))/h`
Also, a function f(x) is said to be differentiable at `x = a` if its L.H.D. and R.H.D. at `x= a` exist and both are equal.
For the function `f(x)={(abs(x-3),xge1),(x^2/4-(3x)/2+13/4,x lt1):}`
answer the following questions:
(i) What is R.H.D. of `f(x)` at `x =1`?
(ii) What is L.H.D. of `f(x)` at `x = 1`?
OR
(iii) (b) Find `f'(2) and f'(-1)`.