Question

Find the inflection point of the function `e^(-x/2)` ?

Answer 1

There are no inflection points.

Explanation:

The inflection point will be where the second derivative equals `0`. By definition, it's when the graph goes from concave up to concave down, or vice versa.

Calling the function `f(x)`, we have:

`f(x) = e^(-x/2)`

`f'(x) = -1/2e^(-x/2)`

`f''(x) = 1/4e^(-x/2)`

If we set this to `0`, we get:

`0 = 1/4e^(-x/2)`

Which doesn't have any solutions because `e^x != 0`. So there are no inflection points.

Hopefully this helps!