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For the function f(x) = 4 loge(x - 1) - 2x2 + 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).
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
For the function f(x) = 4 loge(x - 1) - 2x2+ 4x + 5, x > 1, which o...
It seems like the expression for f(x) is incomplete. Could you please provide the complete expression for f(x)?
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Community Answer
For the function f(x) = 4 loge(x - 1) - 2x2+ 4x + 5, x > 1, which o...


So, maxima occurs at x = 2.
f(2) = 4.0 - 2.22 + 4.2 + 5 = 5
Clearly, f(x) = -1 has exactly 2 solutions.

So, f'(e) - f''(2) > 0
Option C is correct.
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For the function f(x) = 4 loge(x - 1) - 2x2+ 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).Correct answer is option 'C'. Can you explain this answer?
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For the function f(x) = 4 loge(x - 1) - 2x2+ 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).Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about For the function f(x) = 4 loge(x - 1) - 2x2+ 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).Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For the function f(x) = 4 loge(x - 1) - 2x2+ 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).Correct answer is option 'C'. Can you explain this answer?.
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