8) Find a unit vector in the direction that f(x, y, z)=2x² +6xz²-yz³ increases most rapidly at the point (2,-3,1) and find the rate of increase in that direction.

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Q: the temperature (in F) at point (x,y)(measured in miles) is given by  T(x,y)=80-x4 +2x2 y-y2 How…

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Q: Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x2 −0.01y2 where…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 4x sin(xy)…

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Q: F(X, y,z) = 2x -y? +z?

A: F(x,y,z)= 2x-y^2-z^2 at point (4,-4,2) df/dx= 2 df/dy=-2y df/dz= -2z

Q: y - 2)2 + (x-2)2 . Find the direction of heat flow in the plate at the point (2, 1). Heat flows in…

A: Introduction: The gradient of the temperature function at the point is the direction of the greatest…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs for…

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Q: Find the directional derivative of the function f(x, y) = ln(x³ + y³) at the point (3, − 2) in the…

A: Use the gradient of function for finding the directional derivative.

Q: Find the maximum rate of change of f(x, y, z) = x+y/z at the point (1, -3, 5) and the direction in…

A: We will find the maximum rate of change and the direction.

Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…