1) The value of c in Rolle's Theorem for the function f(x) = ex sin x, x Ε [0, π] is A) $\frac{\pi}{6}$ B) $\frac{\pi}{4}$ C) $\frac{\pi}{2}$ D) $\frac{3\pi}{4}$ Answer: Option DExplanation:Since Rolle's theorem is satisfied .'. f'(c) = 0 → ec sin c + cos ec = 0 → ec { sin c +cos c} = 0 .'. sin c + cos c = 0 ($\because e^{c}\neq0$) → tan c = -1 → c = tan-1(-1) = $\pi-\frac{\pi}{4}$ = $\frac{3\pi}{4}$
