Jee Main
Application Of Derivatives
JEE Main 2021 (Online) 1st September Evening Shift
MCQ+4 / -12021
The function \(f(x) = {x^3} - 6{x^2} + ax + b\) is such that \(f(2) = f(4) = 0\). Consider two statements :
Statement 1 : there exists x1, x2 \(\in\)(2, 4), x1 < x2, such that f'(x1) = \(-\)1 and f'(x2) = 0.
Statement 2 : there exists x3, x4 \(\in\) (2, 4), x3 < x4, such that f is decreasing in (2, x4), increasing in (x4, 4) and \(2f'({x_3}) = \sqrt 3 f({x_4})\).
Then
Statement 1 : there exists x1, x2 \(\in\)(2, 4), x1 < x2, such that f'(x1) = \(-\)1 and f'(x2) = 0.
Statement 2 : there exists x3, x4 \(\in\) (2, 4), x3 < x4, such that f is decreasing in (2, x4), increasing in (x4, 4) and \(2f'({x_3}) = \sqrt 3 f({x_4})\).
Then