If the interval in which the function \(f(x) = 4x^3 - 6x^2 - 72x + 30\) is strictly decreasing, is (a, b) then a + b is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1
f is strictly decreasing where \(f'(x) \lt 0\).
\(f'(x) = 12x^2 - 12x - 72\)
\(= 12(x^2 - x - 6)\)
\(= 12(x - 3)(x + 2)\)
The product \((x - 3)(x + 2)\) is negative between its roots, so \(f'(x) \lt 0\) for \(-2 \lt x \lt 3\).
\((a, b) = (-2, 3)\)
\(a + b = -2 + 3 = 1\)
NCERT (2026-27 edition):
Increasing and Decreasing Functions
