Functions

[warped bough]

I characterized the function doing derivative lim for +infinite and 0+ and drawing the graph and now my teacher is asking how can I deduct from this witch one is bigger e^pi or pi^e? Can someone help me?

[young marsh]

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[shadow warren]

e^f(x) = x^1/x is also decreasing for x > e
so, compare (e^pi)^(1/epi) to (pi^e)^(1/epi)

[random timber]

aL

[low echo]

this implies that

$$ e^{\pi/e -1} > \pi/e $$

[random timber]

aL

[low echo]

@warped bough an alternative approach