Understanding Point of Inflection in y = e-x2 Curve: Explanation and Example

[zorro]

Homework Statement

A point of inflection of the curve y = e^-x2 is ?

The Attempt at a Solution

I can't find any. There is only one point x=0 which is a maximum. However there is an answer given

Spoiler

(1/√2,1/√e)

 

[micromass]

You'll need to find the second derivative first. Did you calculate that?

 

[zorro]

You'll need to find the second derivative first.

Why?

 

[micromass]

Why?

Because inflection points are the points where the second derivative is zero...
How else did you define inflection points?

 

[zorro]

How else did you define inflection points?

This is what I know - A point where the first derivative is 0 and the derivative does not change its sign as we go through the point.

 

[micromass]

This is what I know - A point where the first derivative is 0 and the derivative does not change its sign as we go through the point.

That would be a saddle point. A saddle point is a special kind of inflection point. A general inflection point is "a point on the curve where the curvature changes sign" or "a point on the curve where the curve changes from concave upwards to concave downards or vice versa" Check http://en.wikipedia.org/wiki/Inflection_point for more information

In general, an inflection point of a smooth curve is where the second derivative is zero.

 

[zorro]

Thanks! I got it now.