In a study of the survivorship of juvenile garter snakes, a researcher arrived at the model F = 4.2 + 0.008R + 0.102S + 0.017R2 − 0.034S2 − 0.268RS where F is a measure of the fitness of the snake, R is the number of reversals of direction during flight from a predator, and S is the degree of stripedness in the color pattern of the snake.† In Example 5 we calculated ∇F(3, 2), the gradient vector of the snake fitness function F when R = 3 and S = 2. Now calculate the gradient vector of the snake fitness function F when R = 6 and S = 4. In which direction u is the directional derivative of F at (6, 4) a maximum? (Give the direction as a unit vector. Round all values to three decimal places.) u
In a study of the survivorship of juvenile garter snakes, a researcher arrived at the model F = 4.2 + 0.008R + 0.102S + 0.017R2 − 0.034S2 − 0.268RS where F is a measure of the fitness of the snake, R is the number of reversals of direction during flight from a predator, and S is the degree of stripedness in the color pattern of the snake.† In Example 5 we calculated ∇F(3, 2), the gradient vector of the snake fitness function F when R = 3 and S = 2. Now calculate the gradient vector of the snake fitness function F when R = 6 and S = 4. In which direction u is the directional derivative of F at (6, 4) a maximum? (Give the direction as a unit vector. Round all values to three decimal places.) u
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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In a study of the survivorship of juvenile garter snakes, a researcher arrived at the model
F = 4.2 + 0.008R + 0.102S + 0.017R2 − 0.034S2 − 0.268RS
where F is a measure of the fitness of the snake, R is the number of reversals of direction during flight from a predator, and S is the degree of stripedness in the color pattern of the snake.†
In Example 5 we calculated
∇F(3, 2),
the gradient vector of the snake fitness function F when
R = 3
and
S = 2.
Now calculate the gradient vector of the snake fitness function F when
R = 6
and
S = 4.
In which direction u is the directional derivative of F at
(6, 4)
a maximum? (Give the direction as a unit vector. Round all values to three decimal places.)
u =
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