If and , then in
- A.is strictly increasing function
- B.has a local maxima
- C.is strictly decreasing function
- D.is bounded
Show answer and solution
Correct option: A
Solution
f'(x) = 3x² + 2bx + c. The discriminant of f'(x) is (2b)² - 4·3·c = 4b² - 12c = 4(b² - 3c). Since b² < c implies b² < 3c, we have b² - 3c < 0, so the discriminant is negative. Since the leading coefficient (3) is positive and f'(x) has no real roots, f'(x) > 0 for all x ∈ (-∞, ∞), meaning f is strictly increasing everywhere.
[AIEEE 2004]