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The temperature on a surface can be described by the equation T(x, y, z) = 2xy...

The temperature on a surface can be described by the equation T(x, y, z) = 2xy + xy2 z + 12e 2z . Use this function to answer the following questions. Remember to clearly organize your work and indicate your final answer.

(a) Find the direction you should head to achieve the greatest rate of change in temperature at any point.

(b) Find the direction you should head to achieve the greatest rate of change in temperature if you are at P(3,2,3).

(c) Find the maximum rate of change in temperature at P(3,2,3)

(d) Find the rate of change in temperature as you head from P(3,2,3) to Q(0,6,3)

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