Calculate the change in a function f(x,y) = x^2 + 3xy - y^2 if x changes from 2 to 2.05 and y changes from 3 to 2.96

We need the change in the value of f(x, y) = x^2 + 3xy -
y^2 when x changes from 2 to 2.05 and y changes from 3 to
2.96.

Initially f(x, y) = 2^2 + 3*2*3 - 3^2 =
13

When the value of x = 2.05 and y =
2.96

f(x, y) = 2.05^2 + 3*2.05*2.96 -
2.96^2

=> 4.2025 + 18.204 -
8.7616

=> 13.6449

The
change is 13 - 13.6449 = 0.6449

When the
value of x and y is changed, the value of the function
increases by 0.6449.