The maximum value of the function
f(x)=xe^(-x) is?

Explain your answer please!

Question

The maximum value of the function 
f(x)=xe^(-x) is? 

Explain your answer please!

anonymous · Answer

take the derivative
set it equal to zero
solve for x

astrophysics · Answer

You will have to use the product rule $$(fg) = f'g+g'f$$

anonymous · Answer

you get the derivative yet?

anonymous · Answer

or are you having problem setting equal to zero and solving?

anonymous · Answer

so 1e^(-x)+xe^-x

misty1212 · Answer

HI!!

misty1212 · Answer

that looks good 
factor out the common factor of $e^{-x}$

astrophysics · Answer

Ahh a wild misty appears!

anonymous · Answer

I'm a bit lost and confused. haha, sorry.

misty1212 · Answer

lol $\color\magenta\heartsuit$

misty1212 · Answer

you got the derivative a bit wrong, you are off by a minus sign

misty1212 · Answer

the derivative of $e^{-x}$ is $-e^{-x}$ by the chain rule

astrophysics · Answer

You have the second part wrong should be $$e^{-x}-xe^{-x}$$

astrophysics · Answer

Oh this lag, misty is too fast

misty1212 · Answer

should have $$e^{-x}-xe^{-x}$$ what @Astrophysics said

misty1212 · Answer

then you have a common factor in each term of $e^{-x}$ factor it out and ignore it because $e^{-x}$ is never zero

anonymous · Answer

e^-x(1-x) I meant

misty1212 · Answer

lets go slow dear
how would you factor $$x-yx$$?

misty1212 · Answer

or maybe $$\color\magenta \heartsuit-x\color\magenta\heartsuit$$

misty1212 · Answer

yeah that is right

misty1212 · Answer

and since $e^{-x}$ is never zero, all you solve is $1-x=0$ and you are done

anonymous · Answer

-x(1-y)

anonymous · Answer

Thanks very much. I understand this problem now. Sorry for being slow ^^

misty1212 · Answer

you are welcome $$\huge \color\magenta \heartsuit$$