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A Function F Is Defined By F X 2 X 2 3 In 0 2 Which Of The Following

1) f is not derivable in (0, 2) 2) f is continuous in [0, 2] 3) f (0) = f (2) 4) Rolle's theorem is correct in [0, 2] Solution: (4)... View Article

1) x < 1 2) x > 0 3) x < 1/2 4) x > 1/2 Solution: (4) x > 1 / 2 f (x) = 4x4 - 2x + 1 f’ (x) > 0 f’ (x) = 16x3... View Article

1) f is increasing only in the interval (0, π / 2) 2) f is decreasing in the interval (0, π) 3) f attains maximum at x = π / 2 4) f... View Article

1) 0 2) 1 / √x - 1 3) 2√x - 1 - 5 4) None of these Solution: (1) 0 f (x) = √(x – 1) + √{x + 24 – 10√(x – 1)} = √(x – 1) + √{25 +... View Article

1) Satisfies Rolle’s theorem and c = π / 4, so that f’ (π / 4) = 4 2) does not satisfy Rolle’s theorem f’ (π / 4) > 4 3) satisfies... View Article

1) increases everwhere 2) decreases in (0, ∞) 3) increases in (0, ∞) 4) None of the above Solution: (2) decreases in (0, ∞) f (x)... View Article

1) (1, ∞) 2) (-∞, 0) 3) (-∞, ∞) 4) None of these Solution: (1) (1, ∞) f (x) = log (1 + x) - (2x / [2 + x]) f’ (x) = (1 / [1 + x])... View Article

1) b < 1 2) b ≥ 1 3) b > 1 4) b ≤ 1 Solution: f (x) = sin x - bx + c f’ (x) = cosx - b For decreasing function, f’ (x) ≤... View Article

1) increasing 2) decreasing 3) neither increasing nor decreasing 4) do not say anything Solution: (3) neither increasing nor... View Article

1) (0, 1) 2) (1, 2) 3) (2, 3) 4) (1, 3) Solution: (1) (0, 1) f (x) = ax2 + bx + c f (x) = (ax3 / 3) + (bx2 / 2) + cx + d f (x) =... View Article

1) k > 1 2) k > - 1 3) k < 1 4) k < - 1 Solution: (1) k > 1 f (x) = kx - sin x f’ (x) = k - cosx f’ (x) > 0 k... View Article

1) (π / 4, π / 2) 2) (- π / 2, π / 4) 3) (0, π / 2) 4) (- π / 2, π / 2) Solution: (2) (- π / 2, π / 4) f (x) = tan-1 (sin x + cos... View Article

1) 2 log3 e 2) 1/2 loge 3 3) log3 e 4) loge 3 Solution: (1) 2 log3 e By LMVT, f’ (c) = [f (b) - f (a)] / [b - a] = [f (3) - f... View Article

1) (0, 2) 2) (2, 3) 3) (3, 4) 4) (4, 5) Solution: (1) (0, 2) f (x) = x2 e-x f’ (x) = (x2e-x)’ = (2x) e-x + (- e-x) (x2) =... View Article

1) (2, 3) 2) (1, 2) 3) (- 2, 1) 4) (-3, -2) Solution: (3) (- 2, 1) f (x) = 2x3 + 3x2 - 12x + 1 f’ (x) = 6x2 + 6x - 12 = 6 (x2 +... View Article

1) x > 2 and also x > 6 2) x > 2 and also x < 6 3) x > -2 and also x < 6 4) x < - 2 and also x > 6 Solution:... View Article

1) increasing in (-∞ - 2) and in (0, 1) 2) increasing in (-2, 0) and (1, ∞) 3) decreasing in (-2, 0) and (0, 1) 4) decreasing in (-∞,... View Article

1) x < 0 2) x > 0 3) x < 1 4) x > 1 Solution: (1) x < 0 f (x) = (eax + e-ax) (a < 0) f’ (x) = aeax + e-ax (- a)... View Article

1) f is continuous for -2 ≤ x ≤ 2 2) f is not derivable for x = 0 3) f(-2) = f(2) 4) f is not a constant function Solution: (2) f is... View Article

1) strictly increases in the interval (1/2, 2) 2) increases in the interval (0, ∞) 3) decreases in the interval (0, 2) 4) strictly... View Article