For a differentiable function

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

Problem

f

, a student uses the tangent line at

x=1

to approximate

f(1.1)

. The tangent-line calculation gives

2.80

, but the actual value, found with technology, is

f(1.1)=2.78

. Which of the following best describes the concavity of

f

near

x=1

? (a)

f

is concave up because the approximation is an overestimate. (b)

f

is neither concave up nor concave down near

x=1

since the approximation error is small. (c)

f

is concave down because the approximation is an overestimate. (d)

f

is concave down because the approximation is an underestimate.