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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding Slopes in the x- and y-Directions In Exercises 51-54, find the slopes of the surface at the given point in (a) the x-direction and (b) the y-direction.

z = 8 x 2 y 2 ( 1 , 1 , 6 )

Chapter 7, Problem 53RE, Finding Slopes in the x- and y-Directions In Exercises 51-54, find the slopes of the surface at the

(a)

To determine

To calculate: The slopes of the surface z=8x2y2 at the point (1,1,6) in the x-direction.

Explanation

Given Information:

The provided equation of surface is z=8x2y2.

The provided graph of surface is shown below,

Formula used:

The partial derivative of function f(x,y,z) with respect to x is the function xf(x,y,z), that describe the slope in x-direction defined as shown

xf(x,y,z)=limδx0f(x+Δx,y,z)f(x,y,z)Δx

The partial derivative of binary function f(x,y,z) with respect to y is the function yf(x,y,z), that describe the slope in y-direction defined as shown.

yf(x,y,z)=limδy0f(x,y+Δy,z)f

(b)

To determine

To calculate: The slopes of the surface z=8x2y2 at the point (1,2,3) in the y-direction.

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