1) f is continuous in [0, π] 2) f is differentiable in [0, π] 3) f(0) = f(π) 4) Rolle’s theorem is not true in [0, π] Solution: (4)... View Article
1) x = 1 / 3 2) x = 1 / √3 3) x = √3 4) None of these Solution: (3) x = √3 For mean value theorem f’ (c) = [f (b) - f (a)] / [b -... View Article
1) f (x) ≤ 2 2) |f (x)| ≤ 1 3) f (x) = 2x 4) f (x) = 3 for at least on x in [0, 2] Solution: (2) |f (x)| ≤ 1 f’ (c) = [f (x) - f... View Article
1) f is not continuous on [–1, 1] 2) f is not differentiable on (–1, 1) 3) f(–1) ≠f(1) 4) f(–1) = f(1) ≠0 Solution: (2) f is not... View Article