Question

for what intervals is f(x)=e^(-x^2) concave up or concave down?

Answer 1

did you take the derivative twice?

Answer 2

i did.. i got f"(x)=4x^2e^(-x^2)-2e(-x^2)

Answer 3

let me check

Answer 4

\[f'(x)=-2xe^{-x^2}\] right?

Answer 5

yes

Answer 6

ok then you are in good shape

Answer 7

factor out the \(e^{-x^2}\)

Answer 8

you get
\[(4x^2-2)e^{-x^2}\] then it is easy to see where this is positive
as \(e^{-x^2}>0\) always, all you need is the sign of \(4x^2-2\)

Answer 9

my answer still isnt coming out right

Answer 10

\[4x^2-2>0\] or
\[2x^2-1>0\] right?

Answer 11

yes

Answer 12

zeros are at \(x=\pm\frac{1}{\sqrt2}\)

Answer 13

negative between the zeros, positive outside

Answer 14

ohthanks