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.
- $$f ( x , y ) = 9 x ^ { 2 } y ^ { 3 } \text { at } ( 2,1 ) ; R : | x - 2 | \leq 0.2 , | y - 1 | \leq 0.2$$

A) $| E | \leq 13.68576$
B) $| \mathrm { E } | \leq 19.65492$
C) $| \mathrm { E } | \leq 25.09056$
D) $| \mathrm { E } | \leq 19.38816$