# Exercise Solution 4.16

The first order Taylor polynomial of a function *f* of a variable * ^{t}x* about a fixed point

*x*

^{[0]}is:

[s1]

Treating * ^{t}z_{log}* as the function

*f*, we construct a second order Taylor polynomial about an arbitrary point

*x*

^{[0]}:

[s2]

Substituting the specific point^{ t}^{–1}*x*^{ }for *x*^{[0]}, this becomes

[s3]

which is the formula for simple return. We conclude that ^{t}z_{simple} is the first-order Taylor polynomial for * ^{t}z_{log}*.