Here is the problem
Using linear approximation, determine the maximum absolute relative error for the function:
$f(x,y,z) = \frac{−4⋅x^3⋅z}{y^3}$
at (1,3,2), assuming that the relative errors with respect to x, y and z are at most 0.8%, 0.3% and 1.2%, respectively. Give your answer as a percentage.
What I came up with:
So I calculated the partial derivatives with respect to (x,y,z) and came up with the linear approximation equation:
$L(x,y,z) = -\frac{8}{27}-\frac{8}{9}*(x-1)-\frac{4}{27}*(y-3)+\frac{8}{27}*(z-2)$
Then I evaluated L(1.008, 3.009, 2.024) and I got $-\frac{2009}{6750}$
Then I compared this value to the value of $f(1, 3, 2)$ and got the answer of 1.0045% which wasn't correct though. What am I doing wrong here?