$$\mathrm{f}(\mathrm{x})\left\{\begin{array}{c} \frac{1}{\mathrm{x}} ; \mathrm{x} \geq 2 \\ \mathrm{ax}^2+2 \mathrm{~b} ;-2<\mathrm{x}<2 \\ -\frac{1}{\mathrm{x}} ; \mathrm{x} \leq-2 \end{array}\right.$$

Continuous at $$\mathrm{x}=2 \quad \Rightarrow \frac{1}{2}=\frac{\mathrm{a}}{4}+2 \mathrm{~b}$$

Continuous at $$\mathrm{x}=-2 \quad \Rightarrow \frac{1}{2}=\frac{\mathrm{a}}{4}+2 \mathrm{~b}$$

Since, it is differentiable at $$\mathrm{x}=2$$

$$-\frac{1}{x^2}=2 \mathrm{ax}$$

Differentiable at $$x=2 \quad \Rightarrow \frac{-1}{4}=4 a \Rightarrow a=\frac{-1}{16}, b =\frac{3}{8}$$