Question

Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y, z) = tan(2x + 5y + 9z), (2, -8, 4) maximum rate of change direction vector

          Find the maximum rate of change of f at the given point and the direction in which it occurs.
f(x, y, z) = tan(2x + 5y + 9z), (2, -8, 4)
maximum rate of change
direction vector

Added by Michael N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/26/2023

Step 1

The gradient of f(x,y,z) is given by the vector: ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z) Taking the partial derivatives of f(x,y,z) with respect to x, y, and z: ∂f/∂x = 2sec^2(2x+5y+9z) ∂f/∂y = 5sec^2(2x+5y+9z) ∂f/∂z = 9sec^2(2x+5y+9z) Evaluating these partial derivatives at Show more…

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Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,y,z)=tan(2x+5y+9z),(2,-8,4) maximum rate of change direction vector Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,y,z)= tan(2x+ 5y + 9z),(2,-8,4) maximum rate of change direction vector