Case Based MCQ Quiz

Rolle's Theorem: Suppose following three condition hold for function \(\mathrm{y}=f(\mathrm{x})\) :
-1. function is defined and continuous on closed interval \([\mathrm{a}, \mathrm{b}]\);
-2. exists finite derivative \(f^{\prime}(x)\) on interval \((a, b)\);
-3. \(f(\mathrm{a})=f(\mathrm{~b})\).
then there exists point \(\mathrm{c}(\mathrm{a}<\mathrm{c}<\mathrm{b})\) such that \(f^{\prime}(\mathrm{c})=0\).

Based on the above information, answer any four of the following questions.