# Math 116 - Chapter 8 - Calculus of Several Variables

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- Math 116 - Chapter 8 - Calculus of Several Variables

**Created:**2008-12-02

**Last Modified:**2011-07-14

#### Related Textbooks:

Applied Calculus: For the Managerial, Life, and Social Sciences (University of Kansas Edition)1) A set A of ordered pairs of real numbers (x,y) called the domain.

2) A rule that associates with each ordered pair in the domain of ƒ one and only one real number, denoted by z=f(x,y)

and

∂f/∂y=lim h-> f(x, y+k)-f(x,y)/h

y: cost of capital equipment

function ƒ: output of the finished product.

If D(a,b)>0;fxx(a,b)<0 then f(x,y) is a relative max

If D>0;fxx>0, f(x,y) is a rel. min

If D<0 then f(x,y) is a saddle point

If D=0, the test is inconclusive

(1) (x1^2+x2^2)m+(x1+x2)b = x1y1+x2y2+xnyn

(2) (x1+x2+..xn)m+nb = y1 + y2 +...+yn

1. The differentials of the independent variables x and y are dx=∆x and dy=∆y

2. The differential of the dependent variable z is dz=(∂f/∂x)dx+(∂ƒ/∂y)dy

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