A twice-differentiable function satisfies the following: • ,

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

A twice-differentiable function

h

satisfies the following: •

h(4)=10.6

h'(4)=3.1

, and

|h''(x)|\le 6

for

3.9\le x\le 4.3

. •

h(4.25)=11.4

h'(4.25)=2.8

, and

|h''(x)|\le 1.5

for

4.15\le x\le 4.35

. To estimate

h(4.3)

, you may use the tangent line centered at

x=4

or the one centered at

x=4.25

. Which center will yield the smaller maximum possible error? State your choice and briefly justify it.