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CUET
-- Applied Mathematics - Section B2
Calculus
The set of value of k, for which the function $f(x)=kx^3+5$ is decreasing is :
(0, ∞)
(-∞, 0)
(1, ∞)
(-∞, 1)
The correct answer is Option (2) → (-∞, 0)
$f(x)=kx^3+5$
for $f(x)$ to be decreasing, $f'(x)<0$
$⇒k2x^2<0$
$⇒k<0⇒(-∞, 0)$