Solucionario Calculo Una Variable Thomas Finney Edicion 9 179 ● ❲CONFIRMED❳

[ V_{\max}= x^2 y = \Bigl(\frac{2R}{\sqrt{3}}\Bigr)^2 \cdot \frac{2R}{\sqrt{3}} = \frac{4R^2}{3} \cdot \frac{2R}{\sqrt{3}} = \frac{8R^3}{3\sqrt{3}}. ]

[ \left(\frac{x}{2}\right)^2+\left(\frac{x}{2}\right)^2+\left(\frac{y}{2}\right)^2 = R^2 . ] He asked the class to volunteer a solution for Exercise 179

As she walked home, she imagined the inscribed cube—edges perfectly aligned, each corner just touching the sphere—sitting like a gem inside a glass sphere, a concrete reminder that sometimes, the most beautiful solutions are the simplest, and that every calculus problem hides a story waiting to be told. heart thudding like a metronome.

Simplifying gave

[ V'(x) = \frac{4x\bigl(R^2 - \tfrac{x^2}{2}\bigr) - x^3}{\sqrt{R^2 - \tfrac{x^2}{2}}} = \frac{4xR^2 - 2x^3 - x^3}{\sqrt{R^2 - \tfrac{x^2}{2}}} = \frac{4xR^2 - 3x^3}{\sqrt{R^2 - \tfrac{x^2}{2}}}. ] a concrete reminder that sometimes

Plugging this back into the expression for :

Maya wrote the result in bold, underlined it, and added a small smiley face next to it—her personal signature of triumph. The next morning, the professor walked into the seminar room, a stack of papers in his hand. He asked the class to volunteer a solution for Exercise 179. Maya’s hand rose, heart thudding like a metronome.