The temperature at any point in the plane is given by T(x, y)=150/x^2+y^2+3. Wha

Question

The temperature at any point in the plane is given by T(x, y)=150/x^2+y^2+3. What shape are the level curves of T? lines circles parabolas ellipses hyperbolas none of the above At what point on the plane is it hottest? (0,0) What is the maximum temperature? 150/3 Find the direction of the greatest increases in temperature at the point (1, 3). What is the value of this maximum rate of change, that is, the maximum value of the directional derivative at (1, 3)? Find the direction of the greatest decrease in temperature at the pint (1, 3). What is the value of this most negative rate of change, that is, the minimum value of the directional derivative at (1, 3)?

Explanation / Answer

c)

magnitude of maximum rate of change =[(-300/13)2+(-900/13)2]

magnitude of   maximum rate of change =[(90000/169)+(810000/169)]

magnitude of   maximum rate of change =[(900000/169)]

magnitude of maximum rate of change =73

d)

magnitude of   minimum rate of change =[(300/13)2+(900/13)2]

magnitude of   minimum rate of change =[(90000/169)+(810000/169)]

magnitude of   minimum rate of change =[(900000/169)]

magnitude of minimum rate of change =73

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