Comparing Changes in z and dz for a Non-Linear Function

[PsychonautQQ]

Homework Statement

If z=x^2-xy+3y^2 and (x,y) changes from (3,-1) to (2.96,-.95) compare the values of Δz and dz.

The Attempt at a Solution

So I plugged the two given sets of (x,y) into and solved for z and subtracted one from the other and got |.7189|. I don't know what the question means when it says compare it to dz. Since z is a function of two variables how do I do this? To I take the partial with regards to each variable or whaaat? does anyone know what the question is asking?

 

[UltrafastPED]

dz is the differential of z; you will obtain an expression with a dx term and a dy term on the RHS; see your text!

Or http://en.wikipedia.org/wiki/Differential_of_a_function#Differentials_in_several_variables

 

[PsychonautQQ]

so I took the function partial of x and added it to the partial of y. it wants me to compare delta_z with dz. Which numbers should I plug in for dz? The initial values or final?

 

[UltrafastPED]

Try the difference of both!