If y=e^(−x^2)y=e−x2, 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))