Solved: A heat-seeking bug is put down at a point on the xy plane, Mathematics

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A heat-seeking bug is put down at a point on the xy plane

Question: The temperature T (in °C) at any point in the region -10 ≤ x ≤ 10, -10 ≤ y ≤ 10 is given by the function

T (x, y) = 100 - x² - y².

(a) Sketch isothermal curves (curves of constant temperature) for T = 100?C, T = 75?C, T = 50?C, T = 25?C, and T = 0°C.

(b) A heat-seeking bug is put down at a point on the xy plane. In which direction should it move to increase its temperature fastest? How is that direction related to the level curve through that point?

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