1. Some bacteria can sense the "nutritional gradient" and will move in the direction of higher concentration of nutrients. Imagine that such a bacteria is placed at the point P(10, 10) in a dish in which the nutrition concentration is given by by N(x, y) =400 - 2x2-y2. Sketch the path of the bacteria as it swims towards higher concentrations.
2. The temperature field in the neighborhood of (π / 4, 0) is given by T(x, y) = square root 2 e-y cos (x). Find the path followed by a heat seeking particle originating at (π / 4, 0).