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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

Find an equation of the tangent plane to the given surface at the specified point.

1. z = 2x2 + y2 − 5y, (1, 2, −4)

To determine

To find: The equation of the tangent plane to the the surface z=2x2+y25y at the point (1,2,4) .

Explanation

Result used:

“Suppose f has continuous partial derivatives, the equation of the tangent plane to the surface z=f(x,y) at the point P(x0,y0,z0) is zz0=fx(x0,y0)(xx0)+fy(x0,y0)(yy0) ”.

Calculation:

The given surface z=f(x,y)=2x2+y25y . (1)

Take partial derivative with respect to x in the equation (1),

fx(x,y)=2(2x)+00=4x

Thus, the partial derivative of x, fx(x,y)=4x .

Take partial derivative with respect to y in the equation (1),

fy(x,y)=0+2y5(1)=2y5

Thus, the partial derivative of y, fy(x,y)=2y5 .

Obtain the partial derivative of x at the given point (1,2,4) .

fx(x0,y0)=fx(1,2)=4(1)=4

Thus, fx(x0,y0)=4

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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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