At a point , the tangent line to the graph of a differentiable function is used to…

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

Problem

At a point

a

, the tangent line to the graph of a differentiable function

f

is used to approximate nearby function values. If this linear approximation is an underestimate for

x

values close to

a

, which of the following is the best conclusion about

f

x=a

? (a)

f''(a)=0

(b)

f''(a)>0

(c)

f''(a)<0

(d)

f''(a)

does not exist