The function is  .

The function is piecewise function and is continuous for all values of .

We need to check differentiability at and  .

Check for differentiability at :

Find the left hand and right hand limits of  at .

Left hand limit at :

Right hand limit at :

Since left and right hand limits are equal , is differentiable at .

Check for differentiability at :

Find the left hand and right hand limits of  at .

Left hand limit at :

Right hand limit at :

Since left and right hand limits are not equal , is not differentiable at .

Find the derivative of the function.

Find when :

Find when :

Find when :

The derivative of the function .

Graph of the function :

Graph of the function :

The derivative of the function .

Graph of the function :

Graph of the function :              

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