The function f(x) = kx^3 + 6kx^2 + 18x + 17 is increasing on R(set of real numbers) if: Option 1: k (0,3) Option 2: k (0, 3/2) Option 3: k (1/2, 3/2) Option 4: k (1/2, 5/2)

The answer is 'k (0, 3/2)'. View full solution:

Calculus > Application of Derivatives

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The function $f(x) = kx^3 + 6kx^2 + 18x + 17$ is increasing on $\mathbb{R}$(set of real numbers) if:

$k \in (0,3)$

$k \in (0, \frac{3}{2})$

$k \in (\frac{1}{2}, \frac{3}{2})$

$k \in (\frac{1}{2}, \frac{5}{2})$

✅ Correct Option: 2

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