$\"\"$

Statement : Prove that if $\"\"$ for all $\"\"$ in an interval $\"\"$ , then $\"\"$ is a constant function on $\"\"$ .

Rolle $\"\"$ s Theorem :

Let $\"\"$ be a function that satisfies the following three hypotheses.

1. $\"\"$ is continuous on $\"\"$ .

2. $\"\"$ is differentiable on $\"\"$ .

3. $\"\"$ .

Then there is a number $\"\"$ in $\"\"$ such that $\"\"$ .

Constant function is continuous on $\"\"$ and differentiable on $\"\"$ .

Therefore $\"\"$ for any value of $\"\"$ in an interval $\"\"$ .

Statement is true.

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True.