A single tangent line will be used to approximate for every in the interval

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

Problem

A single tangent line will be used to approximate

f(x)=e^{x}

for every

x

in the interval

[0.8,1.2]

. You may choose the point of tangency to be

x_0=0.8,\;0.9,\;1.0,

1.2

. Which choice minimizes the greatest possible absolute error of the resulting approximations on that entire interval? (a)

x_0=0.9

(b)

x_0=1.2

(c)

x_0=1.0

(d)

x_0=0.8