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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
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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Chapter 14 Solutions

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P-14RECh-14 P-15RECh-14 P-16RECh-14 P-17RECh-14 P-18RECh-14 P-19RECh-14 P-20RECh-14 P-21RECh-14 P-22RECh-14 P-23RECh-14 P-24RECh-14 P-25RECh-14 P-26RECh-14 P-27RECh-14 P-28RECh-14 P-29RECh-14 P-30RECh-14 P-31RECh-14 P-32RECh-14 P-33RECh-14 P-34RECh-14 P-35RECh-14 P-36RECh-14 P-37RECh-14 P-38RECh-14 P-39RECh-14 P-40RECh-14 P-41RECh-14 P-42RECh-14 P-43RECh-14 P-44RECh-14 P-45RECh-14 P-46RECh-14 P-47RECh-14 P-48RECh-14 P-49RECh-14 P-50RECh-14 P-51RECh-14 P-52RECh-14 P-53RECh-14 P-54RECh-14 P-55RECh-14 P-56RECh-14 P-57RECh-14 P-58RECh-14 P-59RECh-14 P-60RECh-14 P-61RECh-14 P-62RECh-14 P-63RECh-14 P-64RECh-14 P-65RECh-14 P-1PCh-14 P-2PCh-14 P-3PCh-14 P-4PCh-14 P-5PCh-14 P-6PCh-14 P-7PCh-14 P-8P

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