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Let f(x) be a real valued function, then its

• Left Hand Derivative (L.H.D.) : $\operatorname{Lf}^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a-h)-f(a)}{-h}$
  Right Hand Derivative (R.H.D.) : $\operatorname{Rf}^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}$
  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 are equal.
  For the function $\text{f}(\text{x})=\begin{cases}|\text{x}-3|,\text{x}\geq1\\\\\frac{\text{x}^2}{4}-\frac{3\text{x}}{2}+\frac{13}{4},\text{x}<1\end{cases},$ answer the following questions.
  1. R.H.D. of f(x) at x = 1 is:
  1. 1
  2. -1
  3. 0
  4. 2
  2. L.H.D. of f(x) at x = 1 is:
  1. 1
  2. -1
  3. 0
  4. 2
  3. f(x) is non-differentiable at:
  1. x = 1
  2. x = 2
  3. x = 3
  4. x = 4
  4. Find the value of f'(2).
  1. 1
  2. 2
  3. 3
  4. -1
  5. The value of f'(-1) is:
  1. 2
  2. 1
  3. -2
  4. -1