Please help. I am asked to use a total differential to approximate the change in the values of f from P to Q and then compare the estimate with the actual change in f. I know how to obtain an estimate using the total differential but how do you find the actual change in f?
f(x,y)=x^2+2xy-4x
P(1,2)
Q(1.01,2.04)

Question

Please help. I am asked to use a total differential to approximate the change in the values of f from P to Q and then compare the estimate with the actual change in f.  I know how to obtain an estimate using the total differential but how do you find the actual change in f?
f(x,y)=x^2+2xy-4x
P(1,2)
Q(1.01,2.04)

valpey · Answer

The actual change in f is f(Q)-f(P). 
$$f(P) = 1^2 + 2*1*2-4*1$$$$f(Q) = 1.01^2 + 2*1.01*2.04-4*1.01$$