Question

HELP f(x)=e^(x^2/2) Find asymptotes, extrema, intercepts, points of inflection, and define points of concavity.

Answer 1

\[\large f(x)=0 \qquad \text{Gives Intercepts}\]\[\large f'(x)=0 \qquad \text{Gives Critical Points}\]\[\large f''(x)=0 \qquad \text{Gives Inflection Points}\]

Answer 2

Having trouble with any specific part of the problem? :D Or just the whole thing?

Answer 3

pretty much the whole thing...

Answer 4

If we set the function equal to zero,\[\huge 0=e^{x^2/2}\]
When is an exponential function equal to zero? :)

Answer 5

umm...? So sorry for my ignorance.

Answer 6

We set the function equal to 0, then we solve for x.
The answer is `never`.
An exponential never equals 0.\[\huge 0\neq e^{x^2/2}\]If you're confused about that, here is a graph of our function.
https://www.desmos.com/calculator/kcpivgrcz3
See how it never crosses the x-axis? It never "Intercepts" the axis.

So we have no x-intercept.
How about the y intercept? You can plug x=0 into the function to find where it crosses the y-axis.
Or you can cheat and use the nice graph I pasted :) lol

Answer 7

And the y intercept is (0,1) (by the way, I was sitting here thinking "I cannot think of a situation where an exponential function equals 0!!")

Answer 8

lol :)

Answer 9

You can simply list your intercept as y=1. We know that x=0 since it's the intercept. No need for ordered pair on that one.

Ok for Critical points, you'll need to take the derivative, then set the function equal to zero. Do you know how to take the derivative of this bad boy? :O

Answer 10

...nope.

Answer 11

actually I might