Question

How do I solve this:
x^2 * e^-x = x/e

Answer 1

\[x ^{2}e ^{-x}=\frac{ x }{ e }\]

Answer 2

The left is my f(x) while the right side is a line that tangents the function in x=1
and I'm supposed to show that the two lines cross in (0,0) as well :P

Answer 3

Can you explain why (0,0) would be a point where they meet?

Answer 4

It says so in my paper :P

Answer 5

And when I plot the two on my calculator you see that they cross at (1,1/e) and (0,0)

Answer 6

yes, but looking at those function, how can you logically explain why that happens?

Answer 7

I have no idea!

Answer 8

if you give x the value 0, what does you equation look like?

Answer 9

and the same for 1

Answer 10

\[f_{x} (0) = ???\]

Answer 11

Ah, I see what you mean!
But isn't that the easy way to do it? Try-and-fail-method?
Shouldn't it be a way for me to calculate my way to the answer, like \[x=\pm \sqrt{something}\]

Answer 12

yes

Answer 13

altough i am not sure if you can really do that very well for this function.

Answer 14

\[\Large \frac{ x ^{2} }{ e ^{x} } = \frac{ x }{ e }\]

Answer 15

you could say x=0 so everything is 0, and divide both sides by x to see that 1 is also a solution. But much more than that, not really i guess.

Answer 16

Ok, I guess my professor will just have to settle for that :P Thanks a lot!^^

Answer 17

Maybe: \[\huge (x)(\frac{ x }{ e ^{x} }-\frac{ 1 }{ e })=0\] if you want a proper way to put it.