Problem 6. An insect is very sensitive to temperature. The temperature (in o C) at any point (x, y) (meters east and meters north from origin) is defined by the function T = f(x,y) = 10 + 10 cos(x) sin(xy). The insect's home is 5 meters east and 12 meters south of the origin. %3D A. The insect is at home. Compute the direction the insect should move if it would like to travel in the direction of the highest temperature increase. D The incect noving from itc homo towarde the crigin Compute the rato

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Please answer both parts A and B thoroughly.

Problem 6. An insect is very sensitive to temperature. The temperature (in
C) at any point (x, y) (meters east and meters north from origin) is defined
f (x, y) = 10 + 10 cos(x) sin(xy). The insect's home
by the function T
is 5 meters east and 12 meters south of the origin.
A. The insect is at home. Compute the direction the insect should move if it
would like to travel in the direction of the highest temperature increase.
B. The insect is moving from its home towards the origin. Compute the rate
at which the temperature is changing moving in the direction towards
the origin.
Transcribed Image Text:Problem 6. An insect is very sensitive to temperature. The temperature (in C) at any point (x, y) (meters east and meters north from origin) is defined f (x, y) = 10 + 10 cos(x) sin(xy). The insect's home by the function T is 5 meters east and 12 meters south of the origin. A. The insect is at home. Compute the direction the insect should move if it would like to travel in the direction of the highest temperature increase. B. The insect is moving from its home towards the origin. Compute the rate at which the temperature is changing moving in the direction towards the origin.
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