For a twice-differentiable function

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

Problem

g

, suppose

g''(2)>0

. Which statement best describes the relationship between the local linear approximation

L(x)

x=2

and the actual values of

g(x)

for

x

near

2

? (a)

L(x)

lies above

g(x)

when

x>2

and below

g(x)

when

x<2

. (b)

L(x)

is greater than

g(x)

, so the approximation is an overestimate. (c)

L(x)

is less than

g(x)

, so the approximation is an underestimate. (d) No conclusion can be drawn from the information provided.