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Application of Derivatives question

2022 · 24 Jun · Shift 1 · Q29

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JEE Main
Mathematics
Application of Derivatives
2022 · 24 Jun · Shift 1 · Q29

Application of Derivatives question

2022 · 24 Jun · Shift 1 · Q29

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

For the function

f(x) = 4{\log _e}(x - 1) - 2{x^2} + 4x + 5,\,x \gt 1

, which one of the following is NOT correct?

A
f is increasing in (1, 2) and decreasing in (2, $\infty$ )
B
f(x) = $-$ 1 has exactly two solutions
C
$f'(e) - f''(2) \lt 0$
D
f(x) = 0 has a root in the interval (e, e + 1)

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