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Chapter 12: Q. 21 (page 944)

Let f(x, y) and g(x, y) be functions of two variables with the property that 鈭�f鈭�x=鈭�g鈭�xand 鈭�f鈭�y=鈭�g鈭�yfor every point x,y鈭�R2. What is the relationship between f and g?

Short Answer

Expert verified

The relationship is:fx,y=gx,y.

Step by step solution

01

Given  

Given that: 鈭�f鈭�x=鈭�g鈭�xand鈭�f鈭�y=鈭�g鈭�y

02

To find 

We have to find the relationship between f and g.

03

Calculation 

If 鈭�f鈭�x=鈭�g鈭�xand鈭�f鈭�y=鈭�g鈭�ythen we can say that both x and y parrs of the functions are equal.

We can write it as:fx,y=gx,y

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Most popular questions from this chapter

Prove that a square maximizes the area of all rectangles with perimeter P.

Letz=f(x,y)g(x,y).Showthat鈭�z鈭�x=fx(x,y)g(x,y)鈭�f(x,y)gx(x,y)(g(x,y))2and鈭�z鈭�y=fy(x,y)g(x,y)鈭�f(x,y)gy(x,y)(g(x,y))2

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