Solucionario Calculo Una Variable Thomas Finney Edicion 9 179 [new] ✦ [ HIGH-QUALITY ]

[ 4xR^2 - 3x^3 = 0 \quad\Longrightarrow\quad x\bigl(4R^2 - 3x^2\bigr) = 0. ]

When she stood, the room fell silent. She described the geometry, the substitution of , the elegant reduction to a single‑variable function, and the calculus steps that led to the cube. She finished with the final expression (\displaystyle V_\max= \frac8R^33\sqrt3) and a quick sketch of the inscribed cube inside the sphere. [ 4xR^2 - 3x^3 = 0 \quad\Longrightarrow\quad x\bigl(4R^2

Maya had been wrestling with the problem all semester. It was the sort of question that seemed simple at first glance, then revealed hidden layers like an onion. The statement asked her to , using only one variable. In other words, the box’s height and the side of its base were tied together by the geometry of the sphere, and the challenge was to express the volume in terms of a single unknown, then locate its critical point. The statement asked her to , using only one variable

Using the product rule and the chain rule, she obtained The statement asked her to

Plugging this back into the expression for :

This platform hosts several versions of the 9th-edition solution manual, often titled Calculus Solutions by Thomas 9th Edition Calculus Solutions - Thomas 9th Edition by Suleman Internet Archive: You can find the Instructor's Solutions Manual Part 1

Setting the numerator to zero (the denominator never vanished inside the feasible interval) produced