A hiker is climbing a mountain where the elevation of the mountain (in kilometers) is determined by the (-)² - (H)². (a) What is the shape of the base of the mountain where f(x, y) = 0? Provide both the equation and sketch of the shape with appropriate labels. function [(x, y) = 2- (b) Sketch some contours of the function and indicate the direction of elevation increase and direction of elevation decrease. (c) Suppose a hiker is following the trail at the point (-1,-1), walking in the direction of largest elevation gain. What is the slope of the mountain in the direction the hiker is taking? (d) Suppose the hiker at the point (-1,-1) decides to leave the mountain. Which direction (given by a vector) should the hiker travel to decrease their elevation as fast as possible?
A hiker is climbing a mountain where the elevation of the mountain (in kilometers) is determined by the (-)² - (H)². (a) What is the shape of the base of the mountain where f(x, y) = 0? Provide both the equation and sketch of the shape with appropriate labels. function [(x, y) = 2- (b) Sketch some contours of the function and indicate the direction of elevation increase and direction of elevation decrease. (c) Suppose a hiker is following the trail at the point (-1,-1), walking in the direction of largest elevation gain. What is the slope of the mountain in the direction the hiker is taking? (d) Suppose the hiker at the point (-1,-1) decides to leave the mountain. Which direction (given by a vector) should the hiker travel to decrease their elevation as fast as possible?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 2E
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Hello, can you please help me with all these parts because I have no idea how to do it because I am confused. can you please label the parts so I can follow along, please I need help with all of the parts
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A hiker is climbing a mountain where the elevation of the mountain (in kilometers) is determined by the
2 – ( - )² – (H)².
f(x,y)=2-
(a) What is the shape of the base of the mountain where f(x, y) = 0? Provide both the equation and sketch of
the shape with appropriate labels.
(b) Sketch some contours of the function and indicate the direction of elevation increase and direction of elevation
decrease.
(c) Suppose a hiker is following the trail at the point (-1,-1), walking in the direction of largest elevation gain. What
is the slope of the mountain in the direction the hiker is taking?
(d) Suppose the hiker at the point (-1,-1) decides to leave the mountain. Which direction (given by a vector)
should the hiker travel to decrease their elevation as fast as possible?
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