Find an Upper Bound for the Magnitude |E| of the Error

Multiple Choice

Find an upper bound for the magnitude |E| of the error in the approximation f(x, y) ≈ L(x, y) at the given point over the
given region R.
- $$f ( x , y ) = - 4 x ^ { 2 } + 9 y ^ { 2 } - 9 \text { at } ( - 3 , - 2 ) ; R : | x + 3 | \leq 0.1 , | y + 2 | \leq 0.1$$

A) $| E | \leq 0.18$
B) $| E | \leq 0.27$
C) $| E | \leq 0.36$
D) $| E | \leq 0.09$