Calc 3

Question 1

Suppose that you are climbing a hill whose shape is given by z : 829 0.09x2 0.07y2, and that you are at the point (30180, 300). In which direction should you proceed initially in order to reach the top of the hill fastest? If you climb in that direction, at what angle above the horizontal will you be climbing initially (radian measure)? The temperature at any point in the plane is given by T(x,y) : 120 x2 +y2 + 1 ' (a) What shape are the level curves of T ? o A. ellipses B. hyperbolas C. parabolas D. lines E. circles F. none of the above (l3) At what point on the plane is it hottest? What is the maximum temperature? (c) Find the direction of the greatest increase in temperature at the point (2.3). What is the value of this maximum rate of change, that is, the maximum value of the directional derivative at (2,3)? (d) Find the direction of the greatest decrease in temperature at the point (2,3). What is the value of this most negative rate of change, that is, the minimum value of the directional derivative at (2.3)