Question: Let S be the surface that is the graph of (x, y) = 10 - x 2 - y 2 . Suppose that the temperature

Let S be the surface that is the graph of ƒ(x, y) = 10 - x² - y². Suppose that the temperature in space at each point (x, y, z) is T(x, y, z) = x²y + y²z + 4x + 14y + z.

a. Among all the possible directions tangential to the surface S at the point (0, 0, 10), which direction will make the rate of change of temperature at (0, 0, 10) a maximum?

b. Which direction tangential to S at the point (1, 1, 8) will make the rate of change of temperature a maximum?

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