The function f (x) = x1/x is
1) Increasing in (1, ∞) 2) Decreasing in (1, ∞) 3) Increasing in (1, e) decreasing in (e, ∞) 4)... View Article
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The function f (x) = x + cos x is
1) Always increasing 2) Always decreasing 3) Increasing for a certain range of x 4) None of the above Solution:... View Article
If f (x) = 1 / (x + 1) – log (1 + x), x > 0, then f is
1) An increasing function 2) A decreasing function 3) Both increasing and decreasing function 4) None of the above Solution:... View Article
f (x) = tan-1 (sin x + cos x), – π / 2 ≤ x ≤ π / 2, is increasing in
1) [- π / 4, π / 4] 2) [0, π / 2] 3) [- π / 2, π /... View Article
If f (x) = xex(1-x), then f (x) is
1) increasing on [- 1 / 2, 1] 2) decreasing on R 3) increasing on R 4) decreasing on [-... View Article
The function f (x) = log x / x is increasing in the interval
1) (1, 2e) 2) (0, e) 3) (2, 2e) 4) (1 / e, 2e) Solution: (2) (0, e) f (x)... View Article
If f (x) = sin x – cos x, the function decreasing in 0 ≤ x ≤ 2π is
1) [5π / 6, 3π / 4] 2) [π / 4, π / 2] 3) [3π / 2, 5π /... View Article
On the interval (1, 3) the function f (x) = 3x + (2 / x) is
1) Strictly decreasing 2) Strictly increasing 3) Decreasing in (2, 3) only 4) Neither increasing nor decreasing Solution: (2) Strictly... View Article
Function f (x) = [λ sin x + 6 cos x] / [2 sin x + 3 cos x] is monotonic increasing, if
1) λ > 1 2) λ < 1 3) λ < 4 4) λ > 4 Solution: (4) λ >... View Article
The function which is neither decreasing nor increasing in (π / 2, 3π / 2) is
1) cosec x 2) tan x 3) x2 4) |x – 1| Solution: (1) cosec x
f (x) = {0, when x = 0 and x – 3, when x > 0. 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) = 1 – e–x2/2 is
1) Decreasing for all x 2) Increasing for all x 3) Decreasing for x < 0 and increasing for x... View Article
The function [a sinx + b cos x] / [c sin x + d cos x] is decreasing, if
1) ad – bc > 0 2) ad – bc < 0 3) ab – ad > 0 4) ab... View Article
If f (x) = x2 + ax + 5 is increasing function in (2, 3) then the minimum value of a is…; a ϵ R
1) 2 2) –4 3) –2 4) 4 Solution: (2) –4 f (x) = x2 + ax + 5 f’... View Article
Select the correct statement from (a), (b), (c), (d). The function f (x) = xe1-x
1) Strictly increases in the interval (1 / 2, 2) 2) increases in the interval (0, ∞) 3) decreases in... View Article
If f (x) = x / sin x and g (x) = x / [tan x], where 0 < x ≤ 1, then in this interval
1) Both f (x) and g (x) are increasing functions 2) Both f (x) and g (x) are decreasing functions... View Article
If f (x) = x3 – 10x2 + 200x – 10 then
1) f (x) is decreasing in [ – ∞, 10] and increasing in [10, ∞] 2) f (x) is increasing... View Article
The function f defined by f (x) = (x + 2)e-x is
1) Decreasing for all x 2) Decreasing in (-∞, -1) and increasing (-1, ∞) 3) Increasing for all x 4)... View Article
Which one is the correct statement about the function f (x) = sin 2x
1) f (x) is increasing in (0, π / 2) and decreasing in (π / 2, π) 2) f (x)... View Article
The function f (x) = x3 – 3x2 – 24x + 5 is an increasing function in the interval given below
1) (- ∞, – 2) ⋃ (4, ∞) 2) (- 2, ∞) 3) (- 2, 4) 4) (- ∞, 4)... View Article
