Mathematics

Problem

Let

f(x)=e^{x}

. You need to approximate

f(1.02)

and are considering tangent lines centered at

a_1=1

and

a_2=1.04

. The distances

|1.02-a_1|

and

|1.02-a_2|

are equal. Which center produces the smaller approximation error? Provide the chosen center and justify using the behavior of

f''(x)