Asked by Chris
Find the absolute maximum and minimum values of each function on the given interval. f(x)=x(e^-x)
Answers
Answered by
Damon
df/dx = - x e^-x + e^-x
= 0 for max or min within interval
BUT you did not say the interval
in general
e^-x = x e^x
1 = x is one place where the slope is zero
is the second derivative + or - ?
d^2f/dx^2 = -x(-e^-x) -e^-x - e^-x
= xe^-x -2 e^-x)
= (1/e^x)(x-2)
when x = 1
= (1/e) (-2) which is - so that is a max
now I do not know your interval so you better check the ends., I suspect the linmit of x/e^x ---> 0 as x ---> infinity so that would end up being a minimum
= 0 for max or min within interval
BUT you did not say the interval
in general
e^-x = x e^x
1 = x is one place where the slope is zero
is the second derivative + or - ?
d^2f/dx^2 = -x(-e^-x) -e^-x - e^-x
= xe^-x -2 e^-x)
= (1/e^x)(x-2)
when x = 1
= (1/e) (-2) which is - so that is a max
now I do not know your interval so you better check the ends., I suspect the linmit of x/e^x ---> 0 as x ---> infinity so that would end up being a minimum
Answered by
Damon
Oh and by the way when x = 0 we have 0/1
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.