Question

Partial differentials/Linear approx.

Given that f is a differentiable function with f(2,5)=6, fx(2,5)=1 and fy(2,5)=-1, use a linear approx. to estimate f(2.2, 4.9)

Answer 1

According to the solution manual, the answer is 6.3. I can't seem to get that answer...

Answer 2

i know it follows a taylor feel
\[f(x,y)\approx f+fx~x+fy~y\]
but im missing something

Answer 3

You do this:\[L(x^*,y^*)=[f_x(x_0,y_0)](x^*-x_0)+[f_y(x_0,y_0)](y^*-y_0)+z_0\]
where L is the approximation function, with value at the *'s and the 0's is the original point

Answer 4

fx(x-xo) +fy(y-yo) = 0

fx(x-2) +fy(y-5) = 0

(x-2) - (y-5) = 0

Answer 5

gives me .3, so the 6 needs to be applied

Answer 6

f + fx(x-2) +fy(y-5) gives us 6.3