Problem #22 Consider the following function f, point P, and unit vector u.a. Compute the gradient of f and evaluate it at P.b. Find the unit vector in the direction of maximum increase of f at P.c. Find the rate of change of the function in the direction of maximum increase at P.d. Find the directional derivative at P in the direction of the given vector.f(x,y,z)=xy + yz + xz + 7; P(6,- 6,7);a. Vf(x,y,z) =Vf(6, -6,7)=1.(07/12--1/2)√270b. The unit vector in the direction of maximum increase of f at P is(Type exact answers.)c. The rate of change of the function in the direction of maximum increase at P is(Type an exact answer.)d. The directional derivative at P in the direction of the given vector is(Type an exact answer.)C

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onsider the following function f, point P, and unit vector u. Compute the gradient of f and evaluate it at P. . Find the unit vector in the direction of maximum increase of f at P. Find the rate of change of the function in the direction of maximum increase at P. Find the directional derivative at P in the direction of the given vector. 1 f(x,y,z) = xy + yz + xz + 7; P(6, -6,7); (0, -1/2 + √2)

onsider the following function f, point P, and unit vector u. Compute the gradient of f and evaluate it at P. . Find the unit vector in the direction of maximum increase of f at P. Find the rate of change of the function in the direction of maximum increase at P. Find the directional derivative at P in the direction of the given vector. 1 f(x,y,z) = xy + yz + xz + 7; P(6, -6,7); (0, -1/2 + √2)

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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Question

Problem #22

Consider the following function f, point P, and unit vector u.
a. Compute the gradient of f and evaluate it at P.
b. Find the unit vector in the direction of maximum increase of f at P.
c. Find the rate of change of the function in the direction of maximum increase at P.
d. Find the directional derivative at P in the direction of the given vector.
f(x,y,z)=xy + yz + xz + 7; P(6,- 6,7);
a. Vf(x,y,z) =
Vf(6, -6,7)=
1.
(07/12--1/2)
√2
70
b. The unit vector in the direction of maximum increase of f at P is
(Type exact answers.)
c. The rate of change of the function in the direction of maximum increase at P is
(Type an exact answer.)
d. The directional derivative at P in the direction of the given vector is
(Type an exact answer.)
C

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