$\"\"$

Statement : If $\"\"$ for all $\"\"$ in the domain of $\"\"$ , then $\"\"$ is a constant function.

Consider an example :

The derivative of the function is $\"\"$ and the point is $\"\"$ .

Find the function $\"\"$ .

$\"\"$

Apply anti derivative to the function.

$\"\"$ ( since the rate of change of a constant function is zero )

The function passes through the point $\"\"$ .

$\"\"$

Therefore derivative of a constant function is zero always.

Statement is true.

$\"\"$

True.