Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let b be a real parameter, for which a real valued function f(x) is defined as follows.
f(x) = 
dx here a is real.
(i) If f(x) is monotonic for all real values of x, then set of values of b may consists
A
(– ∞ , 0] a = 0, b = – 1 Remain constant as b increases
B
(– ∞ , –1] ∪ [1, ∞ ) a ∈ R, b = 1 Increases for x > a as b increases
C
[2, ∞ ) a ∈ R, b = –1 Decreases for x > a as b decreases
D
(–1, 1) (ii) If 
exists finitely, then limiting value is (–1/2) (iii) The function f(x) Decreases for x < a as b increases
exists finitely, then limiting value is (–1/2) (iii) The function f(x) Decreases for x < a as b increases
Text Solution
Verified by ExpertsThe correct answer is:
A
Ans.
(i) ,
Sol. (– ∞ , –1] ∪ [1, ∞ ),[2, ∞ )
(ii) ,
Sol. a = 0, b = – 1, limiting value is (–1/2)
(iii) , ,
Sol. Increases for x > a as b increases, Decreases for x > a as b decreases, Decreases for x < a as b increases
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
If f(x) = cos π x + 10x + 3x 2 + x 3 , – 2 ≤ x ≤ 3 then absolute minimum value of f(x) is-
The function f(x) = x 5 – 5x 4 + 5x 3 – 1 has-
The function f(x) = has no extrema. if (n ∈ z)
If x exceeds by its square by the greatest possible quantity then x is-
An extreme value of the function
f(x) = (sin –1 x) 3 + (cos –1 x) 3 (–1 < x < 1) is
Let f(x) = (t + 4) 4 log (t+ 1) dt, then -