Let f (x) satisfy all the conditions of mean value theorem in [0, 2] if f (0) = 0 and |f’ (x)| ≤ 1 / 2 for all x in [0, 2] then
1) f (x) ≤ 2 2) |f (x)| ≤ 1 3) f (x) = 2x 4) f (x) = 3... View Article
Latest Posts
The point where the function f (x) = x2 – 5x – 6 satisfies the condition of Rolle’s theorem is
1) x = 5 2) x = 5 / 2 3) x = 6 4) None of these Solution: (2)... View Article
For the function x + (1 / x), x ∈ [1, 3], the value of c for the mean value theorem is
1) 1 2) √3 3) 2 4) None of these Solution: (2) √3 f (x) = x + (1 /... View Article
A value of c for which the conclusion of mean value theorem holds for the function f (x) = loge x on the interval (1, 3) is
1) 2 log3 e 2) (1 / 2) loge 3 3) log3 e 4) loge 3 Solution: (1) 2 log3... View Article
In the mean value theorem, f (b) – f (a) = f (b – a) f’ (c) if a = 4, b = 9 and f (x) = √x then the value of c is
1) 8.00 2) 5.25 3) 4.00 4) 6.25 Solution: (4) 6.25 f (x) = √x f (a) = √4 =... View Article
From mean value theorem f (b) – f (a) = f (b – a) f’ (x1); a < x1 < b if f (x) = 1 / x, then x1 =
1) √ab 2) [a + b] / 2 3) [2ab / (a + b)] 4) [b – a] / [b... View Article
If f (x) = cos x, 0 ≤ x ≤ π / 2, the real number ‘c’ of the mean value theorem is
1) π / 6 2) π / 4 3) sin-1 (2 / π) 4) cos-1 (2 / π) Solution: (3)... View Article
Rolle’s theorem is not applicable to the function f(x) = |x| defined on [–1, 1] because
1) f is not continuous on [–1, 1] 2) f is not differentiable on (–1, 1) 3) f(–1) ≠ f(1)... View Article
For the function f (x) = ex, a = 0, b = 1, the value of c in mean value theorem will be
1) log x 2) log (e – 1) 3) 0 4) 1 Solution: (2) log (e – 1) [f (b)... View Article
For which, interval, the function [x2 – 3x] / [x – 1] satisfies all the conditions of Rolle’s theorem
1) [0, 3] 2) [–3, 0] 3) [1.5, 3] 4) For no interval Solution: (4) For no interval f (x)... 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 >... View Article
Given function f (x) = [e2x – 1] / (e2x + 1) is
1) Increasing 2) Decreasing 3) Even 4) None of these Solution: (1) Increasing f (x) = [e2x – 1] /... View Article
The function f (x) = tan–1 (sinx + cos x), x > 0 is always an increasing function on the interval
1) (0, π) 2) (0, π / 2) 3) (0, π / 4) 4) (0, 3π / 4) 5) (0,... View Article
Function f (x) = [4x2 + 1] / x is decreasing for interval
1) (-1 / 2, 1 / 2) 2) [-1 / 2, 1 / 2] 3) (-1 , 1) 4) [1,... View Article
For all x ∈ (0, 1)
1) ex < 1 + x 2) loge (1 + x) < x 3) sin x > x 4) loge... View Article
If f (x) = x, – 1 ≤ x ≤ 1, then function f (x) is
1) Increasing 2) Decreasing 3) Stationary 4) Discontinous Solution: (1) Increasing
Let f (x) = x3 + bx2 + cx + d, 0 < b2 < c. Then f
1) Is bounded 2) Has a local maxima 3) Has a local minima 4) Is strictly increasing Solution: (4) Is... View Article
The length of the longest interval, in which the function 3 sin x – 4 sin3 x increasing is
1) π / 3 2) π / 2 3) 3π / 2 4) π Solution: (1) π / 3 Since... View Article
A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?
1) Interval = (- ∞, 1 / 3), Function = 3x2 – 2x + 1 2) Interval = (- ∞,... View Article
The function xx is increasing, when
1) x < 1 / e 2) x > 1 / e 3) x < 0 4) For all real... View Article
