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The Rolle S Theorem Is Applicable In The Interval 1 X 1 For The Function

1) f (x) = x 2) f (x) = x2 3) f (x) = 2x3 + 3 4) f (x) = |x| Solution: (2) f (x) = x2 f (x) = x2 f (1) = f (-1) = 1 f (x) is... View Article

In Which Of The Following Functions Rolle S Theorem Is Applicable

1) f (x) = |x| in - 2 ≤ x ≤ 2 2) f (x) = tanx in 0 ≤ x ≤ π 3) f (x) = 1 + (x - 2)⅔ in 1 ≤ x ≤ 3 4) f (x) = x (x - 2)2 in 0 ≤ x ≤ 2... View Article

The Value Of C In 0 2 Satisfying The Mean Value Theorem For The Function F X X X 1 2

1) 3/4 2) 4/3 3) 1/3 4) 2/3 5) 5/3 Solution: (2) 4/3 f (x) = x(x - 1)2, x ∈ [0, 2] f’ (c) = [f (b) - f (a)] / [b - a] f (2) =... View Article

For What Values Of X Function F X X 4 4x 3 4x 2 40 Is Monotonic Decreasing

1) 0 < x < 1 2) 1 < x < 2 3) 2 < x < 3 4) 4 < x < 5 Solution: (2) 1 < x < 2 f (x) = x4 - 4x3 + 4x2 +... View Article

If F Be A Real Valued Function Defined On The Interval 0 Infinity By

1) f’’ (x) exists for all x ∈ (0, ∞) 2) f’ (x) exists for all x ∈ (0, ∞) and f’ is continuous on (0, ∞) but not differentiable on (0, ∞) 3)... View Article

If F G And H Be Real Valued Functions Defined On The Interval 0 1

1) a = b and c ≠ b 2) a = c and a ≠ b 3) a ≠ b and c ≠ b 4) a = b = c Solution: (4) a = b = c f (x) = x2 ex^2 + e-x^2 f’ (x) =... View Article

If F X 2x 2 X 4 X Belongs To 1 2 Then For Some C 1 2 F C Is Equal To

1) [f (2) - f (0)] / [2 - 0] 2) [f (2) - f (1)] / [2 - (-1)] 3) [f (1) - f (-1)] / [1 - (-1)] 4) None of these Solution: (1) [f (2)... View Article

If F X Kx Cosx Is Monotonically Increasing For All X Belongs To R Then

1) K > - 1 2) K < 1 3) K > 1 4) None of these Solution: (1) K > - 1 f (x) = kx - cos x f’ (x) = k + sinx Since the... View Article

If F X Xe X 1 X Then F X Is

1) increasing on R 2) decreasing on [- (1/2), 1] 3) increasing on [-(1/2), 1] 4) decreasing on R Solution: (3) increasing on [-(1/2),... View Article

The Function F X Ax B Is Strictly Increasing For All Real X If

1) a > 0 2) a < 0 3) a = 0 4) a ≤ 0 Solution: (1) a > 0 f (x) = ax + b f’ (x) = a For strictly increasing, f’(x) > 0... View Article

If F X Then The Function F X Is

If f (x) =then the function f (x) is 1) increasing when x > 0 2) strictly increasing when x > 0 3) strictly increasing at x = 0... View Article

The Function F X X X 2 2 Is Increasing In The Set

1) (-∞, 0) ∪ (2, ∞) 2) (-∞, 1) 3) (0, 1) ∪ (2, ∞) 4) (1, 2) 5) (0, 2) Solution: (3) (0, 1) ∪ (2, ∞) f (x) = [x(x - 2)]2 f’... View Article

The Value Of C In Mean Value Theorem For The Function F X 2x 2 3x 4 In The Interval 1 2 Is

1) 1/2 2) 1/3 3) 3/2 4) 2/3 Solution: (3) 3 / 2 f (x) = 2x2 + 3x + 4 f’ (x) = 4x + 3 f’ (c) = [f (2) - f (1)] / [2 - 1] 4c + 3... View Article

Which Of The Following Functions Is Decreasing On 0 Pi 2

1) sin 2x 2) cos 3x 3) tan x 4) cos 2x Correct option: (4) cos 2x Solution: Let us verify the given options, one by one. (1) sin 2x sin... View Article

Rolle S Theorem Is Applicable In The Interval 2 2 For The Function

1) f (x) = x2 2) f (x) = 4x4 3) f (x) = 2x3 + 3 4) f (x) = π|x| Solution: (2) f (x) = 4x4 f (x) = 4x4, then (i) f (x) is... View Article

If F Is A Real Valued Differentiable Function Such That F X F X 0 For All Real X Then

1) f(x) must be an increasing function 2) f(x) must be decreasing function 3) |f(x)| must be increasing function 4) |f(x)| must be... View Article

The Function X Cot X

1) always increases 2) always decreases 3) never decreases 4) sometimes increases and sometimes decreases Solution: (1) always... View Article

If F X Integral From 0 To X E T 2 T 2 T 3 Dt For All X Belongs To 0 Infinity Then

1) f has a local maximum at x = 2 2) f is decreasing on (2, 3) 3) there exists some c ∈ (0, ∞) such that f '(c) = 0 4) f has a local... View Article

If F X 1 X 2 Sin 2 X X 2 For All R And G X Integral From 1 To X

1) g is increasing on (1, ∞) 2) g is decreasing on (1, ∞) 3) g is increasing on (1, 2) and decreasing on (2, ∞) 4) g is decreasing on... View Article

If f (x) is differentiable and strictly increasing function, then the value of lim_x→0

If f (x) is differentiable and strictly increasing function, then the value of limx→0 [f (x2) - f (x)] / [f (x) - f (0)] is equal to 1) -1 2)... View Article

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