   Chapter 14.4, Problem 1E

Chapter
Section
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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