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e Rock 2100 ft 1969 m 2165 ft mapbox B.T 2428 ft 2494 f 2297 ft- 2955 ft 3418 ft 3543 3215ft 3740ft 2625 165 3281ft 2822 ft D. Greenleaf Hut- 3281ff A. 3412 ft 3412 3609 ft 3675 ft 3872 3675 R ANAA 4005 ft 3872 4331- 4397 Mount Lafayette 5250 ft North Lincoln 5000 ft Mount Lincoln 5089 ft 4528 f 119587 4593f Little Haystack Mountain 4725 ft Map legend | Mapbox © OpenStre

e Rock 2100 ft 1969 m 2165 ft mapbox B.T 2428 ft 2494 f 2297 ft- 2955 ft 3418 ft 3543 3215ft 3740ft 2625 165 3281ft 2822 ft D. Greenleaf Hut- 3281ff A. 3412 ft 3412 3609 ft 3675 ft 3872 3675 R ANAA 4005 ft 3872 4331- 4397 Mount Lafayette 5250 ft North Lincoln 5000 ft Mount Lincoln 5089 ft 4528 f 119587 4593f Little Haystack Mountain 4725 ft Map legend | Mapbox © OpenStre

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please use the second image as reference. This is calculus 3.
4 e Rock 2100 ft 1969 ft 2165ft mapbox BOT 2428 ft 2494 ft 2297 t 2955 ft 3418 ft 35431 3215 ft 40728 2625 ft 393 3281 ft 2822 ft D. Greenleaf Hut- 3281 ft A. 3412ft 3412ft 3609 ft- 3675 ft 3872ft 4003 ft 3675 ft 3872ft 4331 4397 Mount Lafayette 5250 ft North Lincoln 5000 ft Mount Lincoln 5089 ft 4528 ft 4856 ft 4593 ft Little Haystack Mountain 4725 ft Map legend | Mapbox © OpenStre
Transcribed Image Text:4 e Rock 2100 ft 1969 ft 2165ft mapbox BOT 2428 ft 2494 ft 2297 t 2955 ft 3418 ft 35431 3215 ft 40728 2625 ft 393 3281 ft 2822 ft D. Greenleaf Hut- 3281 ft A. 3412ft 3412ft 3609 ft- 3675 ft 3872ft 4003 ft 3675 ft 3872ft 4331 4397 Mount Lafayette 5250 ft North Lincoln 5000 ft Mount Lincoln 5089 ft 4528 ft 4856 ft 4593 ft Little Haystack Mountain 4725 ft Map legend | Mapbox © OpenStre
(b) On the following page is a set of level curves. (i) At the point A, are fe and fy positive or negative? Please explain your answer. (ii) At the point B, is the directional derivative in the direction of the vector positive or negative? Explain. (iii) Find a point where there is a local maximum and label it "C". (iv) Find all global maxima and minima on the path given by the dotted black line. Circle the points that are maxima, and put a square around the ones that are minima. (v) What must be true about the relationship between the level curve passing through the points you listed in (iv) and the dotted path at those points (or, their corresponding tangent vectors)? Please explain using complete sentences. (vi) Suppose your friend wanted to find the steepest path up starting at point D, so they found the gradient vector and kept walking in a straight line in that direction. Where would they end up? Explain what is wrong with this reasoning and draw the path you would take instead. 2
Transcribed Image Text:(b) On the following page is a set of level curves. (i) At the point A, are fe and fy positive or negative? Please explain your answer. (ii) At the point B, is the directional derivative in the direction of the vector positive or negative? Explain. (iii) Find a point where there is a local maximum and label it "C". (iv) Find all global maxima and minima on the path given by the dotted black line. Circle the points that are maxima, and put a square around the ones that are minima. (v) What must be true about the relationship between the level curve passing through the points you listed in (iv) and the dotted path at those points (or, their corresponding tangent vectors)? Please explain using complete sentences. (vi) Suppose your friend wanted to find the steepest path up starting at point D, so they found the gradient vector and kept walking in a straight line in that direction. Where would they end up? Explain what is wrong with this reasoning and draw the path you would take instead. 2
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