Let for . Which of the following describes the sign of for…

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

Problem

Let

H(x)=\displaystyle\int_{x^{2}}^{3x} \sqrt{1+t^{4}}\,dt

for

x>0

. Which of the following describes the sign of

H'(x)

for

x>0

? (a)

H'(x)

is positive for all

x>0

. (b)

H'(x)

is negative for all

x>0

. (c) The sign of

H'(x)

varies depending on the value of

x

. (d)

H'(x)

is positive when

x>1

and negative when

0<x<1