point of inflection question (1 Viewer)

[Mr Chi]

On the curve y= x/e^x find the point of inflection and sketch it.

Can someone show me how to work this out, thanks.

 

[darkliight]

Well we know that if a point (x,y) is a point of inflexion, then the second derivative changes sign at this point. So I guess we'll at least need the second derivative ...

y'(x) = 1/e^x - x/e^x
y''(x) = (x-2)/e^x

Now we know that e^x is never negative (why?), so the only time y''(x) changes sign is at x = 2 (why?) (from negative to positive(why?))

Sub x = 2 into y(x) and we get y = 2/e^2 ~ 1/4
So our point of inflection is (2, 2/e^2)

Graphing is up to you
Hope that helps.

 

[Riviet]

Hope the sketch helps.