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

• Left Hand Derivative (L.H.D.) : $\text{Lf}'(\text{a})=\lim_\limits{\text{h}\rightarrow0}\frac{\text{f}(\text{a}-\text{h})-\text{f}(\text{a})}{-\text{h}}$
  
• Right Hand Derivative (R.H.D.) : $\text{Rf}'(\text{a})=\lim_\limits{\text{h}\rightarrow0}\frac{\text{f}(\text{a}+\text{h})-\text{f}(\text{a})}{\text{h}}$
  

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