Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If f : R → R is a twice differentiable function such that f ′′ (x) > 0 for all x ∈ R, and f 
= 
, f(1) = 1, then
A
f ′ (1) ≤ 0
B
f ′ (1) > 1
C
0 < f ′ (1) ≤ 
D
< f ′ (1) ≤ 1
Text Solution
Verified by ExpertsThe correct answer is:
B
f ′′ (x) > 0 for all x ∈ R , f(1/2) = 1/2, f(1) = 1
⇒ f ′ (x) increases
Let g(x) = f(x) – x , x ∈ [1/2,1]
Then g ′ (x) = 0 has atleast one real root in (1/2,1)
f ′ (x) = 1 has atleast one real root in (1/2,1)
Hence f ′ (x) increases ⇒ f ′ (1) > 1
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