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CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS 87 F 4H 1 2 3 Figure 10.6.4 Contours and gradient for T(x, y) and the missile's path. 10 10 Activity 10.6.6 a. The temperature T(x, y) has its maximum value at the fighter jet's loca- tion. State the fighter jet's location and explain how Figure 10.6.4 tells you this.

CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS 87 F 4H 1 2 3 Figure 10.6.4 Contours and gradient for T(x, y) and the missile's path. 10 10 Activity 10.6.6 a. The temperature T(x, y) has its maximum value at the fighter jet's loca- tion. State the fighter jet's location and explain how Figure 10.6.4 tells you this.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS 87 4 6 8 10 5 9 Figure 10.6.4 Contours and gradient for T(x, y) and the missile's path. Activity 10.6.6 a. The temperature T(x, y) has its maximum value at the fighter jet's loca- tion. State the fighter jet's location and explain how Figure 10.6.4 tells you this. b. Determine VT at the fighter jet's location and give a justification for your response. c. Suppose that a different function f has a local maximum value at (ro, yo). Sketch the behavior of some possible contours near this point. What is Vf(ro, yo)? (Hint: What is the direction of greatest increase in f at the local maximum?) d. Suppose that a function g has a local minimum value at (ro, yo). Sketch the behavior of some possible contours near this point. What is Vg(ro, yo)? e. If a function g has a local minimum at (ro, yo), what is the direction of greatest increase of g at (ro, yo)?
Transcribed Image Text:CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS 87 4 6 8 10 5 9 Figure 10.6.4 Contours and gradient for T(x, y) and the missile's path. Activity 10.6.6 a. The temperature T(x, y) has its maximum value at the fighter jet's loca- tion. State the fighter jet's location and explain how Figure 10.6.4 tells you this. b. Determine VT at the fighter jet's location and give a justification for your response. c. Suppose that a different function f has a local maximum value at (ro, yo). Sketch the behavior of some possible contours near this point. What is Vf(ro, yo)? (Hint: What is the direction of greatest increase in f at the local maximum?) d. Suppose that a function g has a local minimum value at (ro, yo). Sketch the behavior of some possible contours near this point. What is Vg(ro, yo)? e. If a function g has a local minimum at (ro, yo), what is the direction of greatest increase of g at (ro, yo)?
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