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Anyone know how to answer this question? I'm stuck :P

Does the following function have an extremum? If yes, find it. Is it a maximum or minimum?

f(x) = xe^-x

I was thinking of using the product rule to differentiate but i don't know where to go from there
Reply 1
Avatar for Zacken
Zacken
22
Original post by chandmeister
Does the following function have an extremum? If yes, find it. Is it a maximum or minimum?

f(x) = xe^-x

I was thinking of using the product rule to differentiate but i don't know where to go from there


When you differentiate, what do you get? Set the expression you get equal to 0 and solve for xx from there. You're thinking along the right lines.
Reply 2
Avatar for chandmeister
chandmeister
OP
Original post by Zacken
When you differentiate, what do you get? Set the expression you get equal to 0 and solve for xx from there. You're thinking along the right lines.


When I differentiated I got e^-x -xe^-x. I then equated it to zero and took a common factor of e^-x out to get this:

e^-x (1-x) = 0

then i got that x=1 and f(1) = 1/e so the extremum i believe is (1,1/e)

The other bit is pretty self explanatory at this point. Thanks for your help!
Reply 3
Avatar for Zacken
Zacken
22
Original post by chandmeister
When I differentiated I got e^-x -xe^-x. I then equated it to zero and took a common factor of e^-x out to get this:

e^-x (1-x) = 0

then i got that x=1 and f(1) = 1/e so the extremum i believe is (1,1/e)

The other bit is pretty self explanatory at this point. Thanks for your help!


Perfect.

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