The derivative of a twice-differentiable function is increasing on the interval and…

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

Problem

The derivative

h'(x)

of a twice-differentiable function

h

is increasing on the interval

(-3,1)

and decreasing on the interval

(1,4)

. Which statement about the concavity of

h

is most accurate? (a)

h

is concave up on

(-3,1)

and concave down on

(1,4)

, but there is no point of inflection at

x=1

because

h'(1)

might not be zero. (b)

h

is concave up on

(-3,1)

and concave down on

(1,4)

, with a possible point of inflection at

x=1

. (c)

h

is concave down on

(-3,1)

and concave up on

(1,4)

, with a possible point of inflection at

x=1

. (d)

h

is concave up on the entire interval

(-3,4)

, so there is no point of inflection on that interval.