The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.

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The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be (– $\infty$, 6). Explanation: f(x) = 5 + 36x – 3x2 Differentiate w.r. to ‘x’ f'(x) = 0 + 36 – 6x For increasing function f'(x) > 0 \implies 36 – 6x > 0 \implies 36 > 6x \implies x < 6 i.e., x ∈ (– $\infty$, 6) Hence f(x) increases in (– $\infty$, 6).

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