Both parts of this problem refer to the function f(x, y, z) = x2 + y3 + 5z. (a) Find the directional derivative of f(x, y, z) at the point (1, 1, −2) in the direction of the vector <(1/√(3)), −(1/√(3)), (1/√(3))> (b) Find an equation of the tangent plane to the level surface of f for the function value −8 at the point (1, 1, −2).

Both parts of this problem refer to the function f(x, y, z) = x2 + y3 + 5z. (a) Find the directional derivative of f(x, y, z) at the point (1, 1, −2) in the direction of the vector <(1/√(3)), −(1/√(3)), (1/√(3))> (b) Find an equation of the tangent plane to the level surface of f for the function value −8 at the point (1, 1, −2).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 30E

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