3. An insect is moving on the ellipse 2x + y? = 3 on the ry-plane...

Transcribed Image Text:

3. An insect is moving on the ellipse 2x + y? = 3 on the ry-plane in the clockwise direction at a constant speed of 3 centimeter per second. The temperature function T(x, y) (experienced by the insect) is given by T(x, y) = 3x2 - 2yx, where T is measured in degree Celsius and r, y are measured in centimeters. What is the rate of change of the temperature (in degree Celsius per second) when the insect is at the point (1, 1)? Hint: Let f(x, y) f(x, y) = 3 at the point (1, 1). Using this information, how can we easily find a vector which is tangential to the ellipse f(x, y) = 3 and is pointing in the clockwise direction? Take note the directional derivative has unit degree Celsius per centimeter NOT degree Celsius per second. = 2.x2 + y?. The gradient vector Vf(1, 1) = (4, 2) is normal to the ellipse 3. An insect is moving on the ellipse 2x + y? = 3 on the ry-plane in the clockwise direction at a constant speed of 3 centimeter per second. The temperature function T(x, y) (experienced by the insect) is given by T(x, y) = 3x2 - 2yx, where T is measured in degree Celsius and r, y are measured in centimeters. What is the rate of change of the temperature (in degree Celsius per second) when the insect is at the point (1, 1)? Hint: Let f(x, y) f(x, y) = 3 at the point (1, 1). Using this information, how can we easily find a vector which is tangential to the ellipse f(x, y) = 3 and is pointing in the clockwise direction? Take note the directional derivative has unit degree Celsius per centimeter NOT degree Celsius per second. = 2.x2 + y?. The gradient vector Vf(1, 1) = (4, 2) is normal to the ellipse