An insect is moving on the ellipse 2x² + y² = 3 on the xy-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 x, 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) = 2x² + y². The gradient vector Vƒ(1, 1) = (4,2) is normal to the ellipse 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.
An insect is moving on the ellipse 2x² + y² = 3 on the xy-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 x, 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) = 2x² + y². The gradient vector Vƒ(1, 1) = (4,2) is normal to the ellipse 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.
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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Transcribed Image Text:An insect is moving on the ellipse 2x² + y² = 3 on the xy-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 x, 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) 2x² + y². The gradient vector Vf(1, 1) = (4,2) is normal to the ellipse
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.
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