The function $\"\"$

If $\"\"$ is differentiable at $\"\"$ , then it should be continuous at $\"\"$ .

$\"\"$ is a polynomial function in the two intervals, therefore it is continuous at all points in the given intervals .

Check for differentiability at $\"\"$ :

Find the left hand and right hand limits of $\"\"$ at $\"\"$ .

Left hand limit:

$\"\"$ .

Right hand limit:

$\"\"$

Since left and right hand limits are not equal , So $\"\"$ is discontinuous at $\"\"$ .

Therefore, $\"\"$ is not differentiable at $\"\"$ .

Find the derivative of the function.

Find $\"\"$ when $\"\"$ :

$\"\"$

Find $\"\"$ when $\"\"$ :

$\"\"$

The derivative of the function $\"\"$ .

Graph of the function $\"\"$ :

$\"\"$

Graph of the function $\"\"$ :

$\"\"$

The given function is not differentiable at $\"\"$ .

Graph of the function $\"\"$ is

$\"\"$

Graph of the function $\"\"$ is

$\"\"$ .