Question
Question: If f(x) = x<sup>3</sup> + ax<sup>2</sup> + bx + c attains it's local minimum at certain negative re...
If f(x) = x3 + ax2 + bx + c attains it's local minimum at
certain negative real number then –
A
a2 – 3b > 0, a < 0, b < 0
B
a2 – 3b > 0, a < 0, b > 0
C
a2 – 3b > 0, a > 0, b < 0
D
) a2 – 3b > 0, a > 0, b > 0
Explanation
Solution
)
Sol. f(x) = 3x2 + 2ax + b
Let f(x) = 0 at x = a, b (B > r) then
f '(x) = 3(x – a) (x – b)
f(x) is minimum at x = b < 0
Q D > 0 Ž 4a2 – 12b > 0, 
, b > 0
Ž a2 – 3b > 0, a > 0, b > 0