I have math exam tomorrow and i need some help.

GrP

excuse me for my bad english, but i'm trying hard.

1. function f(x), for x>0 is defined with:

f(x)=(x^4)^(x^2)

^ - potency

find stationary points of the function f(x) on the interval (0,infinite).

what exactly do i do here?
do i use logarithm on both sides, and then i get:

log(y)=(x^2)*log(x^4)

and then i different (differential) both sides, and set y'=0
and i calculate x?
is this right so far?

now i want to get local min. and max.
and i different again, and then what?
and i need to find out if these points are globlal min and max.

2. integral from 1 to infinity (((x^2+1)^(1/2))/((x^3)*(x^2-1)^(1/2)))dx

and ideas what could i do? what would "u" be? (u^2)=(x^2)+1?

thank you!

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whozum

1. Thats right so far.
2.

$$\int_1^{\infty} \frac{\sqrt{x^2+1}}{x^3\sqrt{x^2-1}}dx$$

Well first off, you'll need to do an improper integral.

First thing I would try is a trig substitution, then maybe look at it by parts if that doesn't work. u = x^2 might get you somewhere but I don't know.

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