Let be a positive

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

Problem

Let

f

be a positive, increasing, differentiable function on

(0,\infty)

. Define

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

for

x>0

. Which of the following must be true for all

x>0

? (a)

G'(x)=0

(b)

G'(x)<0

(c)

G'(x)>0

(d) The sign of

G'(x)

cannot be determined from the given information.