Let the function f(x) = x/3 + 3/x + 3, x ≠ 0 be strictly increasing in (-∞, α₁) (α₂, ∞) and strictly decreasing in (α₁, α₂) (α₄, α₅). Then Σ i=1 ⁵ α i ² is equal to:

Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q203

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let the function

f(x) = \frac{x}{3} + \frac{3}{x} + 3, \; x \ne 0

be strictly increasing in

(-\infty, \alpha_1) \cup (\alpha_2, \infty)

and strictly decreasing in

(\alpha_1, \alpha_2) \cup (\alpha_4, \alpha_5)

. Then

\sum_{i=1}^{5} \alpha_i^2

is equal to: