The function f(x) = x^3 - 27x + 5 is strictly decreasing in the inter…

The correct answer is Option (4) → \((-3, 3)\)

A function is strictly decreasing where \(f'(x) \lt 0\).

    \(f'(x) = 3x^2 - 27\)
    \(f'(x) = 3(x^2 - 9)\)
    \(f'(x) = 3(x - 3)(x + 3)\)

The sign of f’(x) changes at x = −3 and x = 3:

    \(x \lt -3\): both factors negative, \(f'(x) \gt 0\)
    \(-3 \lt x \lt 3\): factors of opposite signs, \(f'(x) \lt 0\)
    \(x \gt 3\): both factors positive, \(f'(x) \gt 0\)

So f is strictly decreasing in (−3, 3) and strictly increasing in \((-\infty, -3)\) and in \((3, \infty)\).