   Chapter 14.6, Problem 10E

Chapter
Section
Textbook Problem

(a) Find the gradient of f.(b) Evaluate the gradient at the point P.(c) Find the rate of change of f at P in the direction of the vector u.10. f(x, y, z) = y2exyz, P(0, 1, −1), u = ⟨ 3 13 , 4 13 , 12 13 ⟩

(a)

To determine

To find: The gradient of f(x,y,z)=y2exyz .

Explanation

Calculation:

The given function is, f(x,y,z)=y2exyz .

The gradient of f(x,y,z) is computed as follows,

f(x,y,z)=fx(x,y,z),fy(x,y,z),fz(x,y,z)=fx(y2exyz),fy(y2exyz),fz(y2exyz)=(y2yzexyz

(b)

To determine

To evaluate: The gradient of f(x,y,z)=y2exyz at the point P(0,1,1) .

(c)

To determine

To find: The rate of change of f(x,y,z)=y2exyz at the point (0,1,1) and in the direction of the vector, u=313,413,1213 .

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