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.
- $$\mathrm { f } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = 4 \mathrm { xy } + 8 \mathrm { yz } + 10 \mathrm { zx } \text { at } ( 1,1,1 ) ; \mathrm { R } : | \mathrm { x } - 1 | \leq 0.1 , | \mathrm { y } - 1 | \leq 0.1 , | \mathrm { z } - 1 | \leq 0.1$$

A) $| \mathrm { E } | \leq 0.45$
B) $| \mathrm { E } | \leq 0.42$
C) $| \mathrm { E } | \leq 0.35$
D) $| \mathrm { E } | \leq 0.375$