Let f(x) = x2+ 3ax + 4, x ∈ [-1, 6] . The range of a. for which f(x) is strictly decreasing function is :
Answer & explanation
Correct answer: option 2
f'(x) = 2x + 3a
∵ f(x) is strictly decreasing
∴ f'(x) < 0 ⇒ 2x + 3a < 0
$⇒ x < \frac{-3a}{2}$
∵ x ∈ [-1, 6]
the maximum value of a for f to be decreasing on (-1,6) is given by, $a_{max} = \frac{-2\times 6}{3}=-4$
∴ Range of a (-∞, -4)