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Unformatted text preview: V (2 ,y ). Please label your axes and mark several points on each axis. Figure 1: V (2 ,y ) = 3 π (4y 2 ) (b) Graph the single variable function V ( x, 1). Please label your axes and mark several points on each axis. Figure 2: V ( x, 1) = 3 π ( x 21) (c) Explain in the context of the problem what the graphs in (a) and (b) tell you about the volume of material needed to construct a pipe as a function of the two radi. How does the volume of material needed change as a function of x , the outer radius? As a function of the inner radius y ? Solution: The volume of material needed to make the pipe is a decreasing function of the inner radius and an increasing function of the outer radius. Page 2...
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 Spring '10
 rosanna
 Order theory, Monotonic function, Convex function, outer radius

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