   Chapter 7.4, Problem 43E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Using First Partial Derivatives In Exercises 41-44, find all values of x and y such that f x ( x , y ) = 0 and f y ( x , y ) = 0 simultaneously. f ( x , y ) = 1 x + 1 y + x y

To determine

To calculate: The all value of x and y from the function f(x,y)=1x+1y+xy such that fx(x,y)=0 and fy(x,y)=0 simultaneously.

Explanation

Given information:

The provided function is f(x,y)=1x+1y+xy and the condition is fx(x,y)=0 and fy(x,y)=0 simultaneously.

Formula used:

Consider the function z=f(x,y) then for the value of zx consider y to be constant and differentiate with respect to x and the value of zy consider x to be constant and differentiate with respect to y.

Calculation:

Consider the provided function is,

f(x,y)=1x+1y+xy

Partially derivative of the function f(x,y)=1x+1y+xy with respect to x.

fx(x,y)=x(1x+1y+xy)=x(1x)+1yx(1)+yx(x)=1x2+y

Substitute 0 for fx(x,y).

1x2+y=01=x2yx2y=1y=1x2

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