2. Let P(1,1,1) be a point, f(x, y, z) and g(x, y, z) be two differentiable functions satisfying the lowing conditions: i) f(P) = 2 and g(P)=5 ng ii) =-1 iii) f(x, y,z) increases most rapidly at the point P(1,1,1) in the direction of u=i-87+4k and the maximum rate of increase is 6. iv) The equation of the tangent plane to the surface of f(x, y, z) + 2 g(x, y, z) = 12 at the point P(1, 1,1) is

2. Let P(1,1,1) be a point, f(x, y, z) and g(x, y, z) be two differentiable functions satisfying the lowing conditions: i) f(P) = 2 and g(P)=5 ng ii) =-1 iii) f(x, y,z) increases most rapidly at the point P(1,1,1) in the direction of u=i-87+4k and the maximum rate of increase is 6. iv) The equation of the tangent plane to the surface of f(x, y, z) + 2 g(x, y, z) = 12 at the point P(1, 1,1) is

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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2. Let P(1,1,1) be a point, f(x, y, z) and g(x, y,z) be two differentiable functions satisfying the
following conditions:
i) f(P) = 2 and g(P) = 5
ng
ii)
= -1
iii) f(x,y,z) increases most rapidly at the point P(1, 1, 1) in the direction of u i-8 j+4k and the
maximum rate of increase is 6.
iv) The equation of the tangent plane to the surface of f(x, y, z)+ 2 g(x, y, z) =12 at the point P(1,1,1) is
og
4x+2y+3z =9. Find the value of
according to these conditions.

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