A twice-differentiable function has a first derivative that decreases on and increases on

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

Problem

A twice-differentiable function

h

has a first derivative

h'

that decreases on

(-3,1)

and increases on

(1,5)

. Which statement about

h

is most accurate? (a)

h

is concave up on

(-3,5)

, so no inflection point occurs at

x=1

. (b)

h

changes from concave down to concave up at

x=1

, so

x=1

is an inflection point. (c)

h

changes from concave up to concave down at

x=1

, so

x=1

is an inflection point. (d)

h'

has a relative minimum at

x=1

, so

h

must be decreasing there and cannot have an inflection point.