Published by:
CGP EDU Academic Team
Published on: August 13, 2026
f(x) = 4 log e (x - 1) -2x 2 + 4x +5, x > 1, which one of the following is NOT correct ?
A
f is increasing in (1, 2) and decreasing in (2, 
)
)
B
f(x)= -1 has exactly two solutions
C
f (e) -f'' (2) < 0
D
f(x) = 0 has a root in the interval (e, e +1)
Text Solution
Verified by ExpertsThe correct answer is:
C
f(x) = 4 log e (x - 1) -2x 2 + 4x +5, x > 1
For l<x<2 
f'(x)>0
For x > 2 
f'(x) < 0 (option 1 is correct)
f (x) = -1 has two solution (option 2 is correct)
f(e)>0
f (e +1) < 0
f (e).f (e +1) < 0 (option 4 is correct)
f ’ (e)-f"(2) = 
-4(e-l) + 8>0
(option C is incorrect)
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