## Function

f(x,y) = py+q

## Domain

xandyare elements of the set of allReal numbers

## Graphs

## Derivative

With respect tox:0

With respect toy:pCritical points are formed where the two derivatives equal 0. These critical points may be minimums, maximums, or saddle points. In the first graph, for

y,p= 1 and will never equal 0. Therefore, there will be no critical points for this graph. This is shown since there is no saddle point and the curve goes from negative to positive infinity.

## Integral

With respect tox:(py + q)x

With respect toy:(^{1}/_{2})py^{2}+ qy

## Interesting Features

This function is a plane that has a constant value for

zfor allxvalues fory. This plane goes up at a constant value. This "slope" is scaled byp. Theqvalue changes the intercept value. Asqincreases, the position of the plane is lifted.

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