Mathematics

Mathematics

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

.

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