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The increase in revenue is calculated as: - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 g'(x) = 3x^2 - 4

📌 Setting \( g'(x) = 0 \):

📌 3x^2 - 4 = 0 \implies x^2 = \frac{4}{3} \implies x = \pm \frac{2}{\sqrt{3}} \approx \pm 1.1547

📌 Evaluate \( g(x) \) at these critical points:

📌 At \( x = \frac{2}{\sqrt{3}} \):

📌 g\left(\frac{2}{\sqrt{3}}\right) = \left(\frac{8}{3\sqrt{3}}\right) - 4\left(\frac{2}{\sqrt{3}}\right) + 2 = \frac{8 - 24 + 6\sqrt{3}}{3\sqrt{3}} = \frac{-16 + 6\sqrt{3}}{3\sqrt{3}}

📌 This is negative, and at \( x = -\frac{2}{\sqrt{3}} \), it's positive. Since \( g(1) = -1 \) and \( g(2) = 2 \), there is a root in \( (1, 2) \), and by symmetry and behavior, another real root exists (confirm via intermediate value theorem or graphing).

📌 Alternatively, use cubic formula or numerical solvers:

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