A differentiable function is positive and strictly decreasing on the interval

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

A differentiable function

f

is positive and strictly decreasing on the interval

(1,4)

. For the accumulation function

g(x)=\int_{2}^{x} f(t)\,dt

, which statement about the graph of

g

(1,4)

is most accurate? (a)

g

is increasing and concave up on

(1,4)

. (b)

g

is decreasing and concave up on

(1,4)

. (c)

g

is increasing and concave down on

(1,4)

. (d)

g

is decreasing and concave down on

(1,4)