For the function $f(x) = 4{\log _e}(x - 1) - 2{x^2} + 4x + 5,\,x > 1$, which one of the following is NOT correct?

Question

For the function

$f(x) = 4{\log _e}(x - 1) - 2{x^2} + 4x + 5,\,x > 1$, which one of the following is NOT correct?

f is increasing in (1, 2) and decreasing in (2, $\infty$)

f(x) = $-$1 has exactly two solutions

$f'(e) - f''(2) < 0$

f(x) = 0 has a root in the interval (e, e + 1)

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