A deflection function (in millimeters) for a steel beam is twice-differentiable on…

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A deflection function

d

(in millimeters) for a steel beam is twice-differentiable on the interval

1\le x\le1.3

meters. Measurements show that

|d''(x)|\le 0.04

for all

x

in this interval. The tangent line to

d

x=1

is used to approximate

d(1.2)

. What is the largest possible magnitude of the error of this approximation? (a)

0.004\text{ mm}

(b)

0.008\text{ mm}

(c)

0.0008\text{ mm}

(d)

0.0016\text{ mm}