For , the tangent line at is used to approximate . Given that for all , determine an…

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

For

f(x)=\sin x

, the tangent line at

x=0

is used to approximate

\sin(0.32)

. Given that

|f''(x)|\le 1

for all

x

, determine an upper bound on the magnitude of the error of this approximation.