# If # y=e^(−x^2)#, what are the points of inflection, concavity and critical points?

##### 1 Answer

#### Explanation:

Given:

we can calculate the first and second order derivatives:

we can therefore determine that:

(1) By solving the equation:

we can see that

Looking at the second derivative, we can see that

(2)

#2x^2-1 = 0 => x=+-1/sqrt(2)#

(3) As

#f(x)# is concave up in#(-oo,-1/sqrt(2))# and in#(1/sqrt(2),+oo)#

#f(x)# is concave down in#(-1/sqrt(2),1/sqrt(2))#