For a controlled experiment, the temperature at a point (x,y,z) is given by 7(x, y, z) = 3x² + y. We have a cylindrical iron pipe with its axis along y-axis and radius 3 units (-axis is passing through its center). The pipe is cut with an iron plate given by the equation 4x-3y=9. Obtain the maximum and minimum temperature at the cross-sectional curve using Lagrange multiplier method.
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