Question
Question: If f(x) = x<sup>3</sup> + bx<sup>2</sup> + cx + d, 0 \< b<sup>2</sup>\< c, then f(x) is –...
If f(x) = x3 + bx2 + cx + d, 0 < b2< c, then f(x) is –
A
Strictly increasing
B
Locally maximum
C
Locally minimum
D
Bounded
Answer
Strictly increasing
Explanation
Solution
f ¢(x) = 3x2 + 2 bx + c
By B2 – 4ac = 4b2 – 12 c
= 4 (b2 – 3c) < 0 as b2 < c
a > 0, D < 0
̃ f ¢(x) > 0 ∀ x.
̃ x is strictly increasing.