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

1. 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
2. (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 from there. You're thinking along the right lines.
3. (Original post by Zacken)
When you differentiate, what do you get? Set the expression you get equal to 0 and solve for 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!
4. (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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