# Maximum Volume of a Right Circular Cylinder

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What is the maximum possible volume of a right circular cylinder with a total surface area (including the top and the bottom)?

600 pi in^2

Find the exact coordinates of the inflection points and critical points of the function (Figure 15.1) on the interval (-10, 10)

f(x)= 2x^3+ 3x^2- 180x+ 150

Find dx/dt given

x=^/Â¯(1+cot3t)

Sketch, the graph of f(x). Identify all extrema, inflection points, intercepts, and asymptotes. Show the concave structure clearly and note any discontinuities.

f(x)x^2/x-1

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#### Solution Summary

The maximum volume of a right circular cylinder is found using derivatives and inflection points. The solution is detailed and well presented.

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