locate the three inflexion points of the curve y=xe^(-x^2).

please show explanation :)

Question

locate the three inflexion points of the curve y=xe^(-x^2).

please show explanation :)

anonymous · Answer

$$y=x*e^{-x^2}$$$$y'=e^{-x^2}(1-2x^2)$$$$y''=2e^{-x^2}x(2x^2-3)$$
$$y''=0  \rightarrow x=\pm \sqrt{3/2}$$

anonymous · Answer

and x = 0

anonymous · Answer

When i diffrentiated y=x∗e−x2 i got y′=e−x2(1+2x2) can you show me how u got the first derivative

anonymous · Answer

use the product rule on x and e^(-x^2) and then the chain rule on e^(-x^2)

anonymous · Answer

i think you misused a sign somewhere for the quantity (1 + 2x^2)

anonymous · Answer

i dont see where i went wrong heres my working out

y'= uv'+vu'

where 

u= x
u'= 1
v=e^(-x^2)
v'=2xe^(-x^2)

then 

y'= x(2xe^(-x^2))+e^(-x^2)(1)

= e^(-x^2)(2x^2+1)

can u tell me where my mistake is

anonymous · Answer

e should be -e

anonymous · Answer

v' is -2x e^(-x^2)

anonymous · Answer

oh yes i see that mistake thanks heaps