Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If f(x) and g(x), 0 ≤ x ≤ 1 be differentiable functions such that f(0) = 2 g(0) = 0, f(1) = 6, g(l) = 2 then in (0,1)
A
f '(x) = 0 
x ∈ R
x ∈ R
B
f ' (x) = 2g'(x), for at least one value of x in (0,1)
C
0
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
B
By LMVT; f '(x) = 
= 6 – 2 = 4
g'(x) 
= 
= 2
⇒ f ' (x) = 2g' (x) for at least one value of x in (0,1)
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 -