Question

Let f(x)=e^−x^2.
(a) What horizontal or vertical asymptotes does f(x) have?
(b) Find the intervals of increase or decrease.
(c) Find the local maximum and minimum values. (d) Where is f(x) concave downward?
(e) Where are the inflection points?

Answer 1

can you write the eqaution out with the drawing tool.. im sorry but i think it would make the equation much more clear

Answer 2

\[f(x)=e^{-x^2}\] like this ?

Answer 3

yes

Answer 4

kk ! now tell me can you find
\[\lim_{x \rightarrow \pm \infty} f(x)\] ?!

Answer 5

I believe it is 0 for both

Answer 6

good ! So is it finite ?! ( just answer) what can you say about the asymptotes of "f" ?!

Answer 7

the horizontal asymptote is 0 and so is the vertical

Answer 8

there is no vertical asymptote ! !
\[\lim_{x \rightarrow \pm \infty}f(x)=a \]
finite ! y=a is an horizontal asymptote ! so y=0 is the horizontal asymptote !
now ! if \[\lim_{x \rightarrow a}f(x)= \pm \] ! then you can say x=a is a verttical asymptote !
now ! we agree that y=0 is the only asymptote of 'f'
is that clear ?!

Answer 9

**\[\lim_{x \rightarrow a}f(x)= \pm \infty \]

Answer 10

ok that makes sense

Answer 11

@fheard still there ?!

Answer 12

yeah but then how do I find increase or decrease

Answer 13

you can't put -infinity,a and a,infinity can you?

Answer 14

wait a is 0 right

Answer 15

yes ! you're right ! okk can you calculate f' (the derviative) ...and see where It's negative and positive kk ?!

Answer 16

still there ! ?

Answer 17

yeah the derivative is -2x*e^-x^2

Answer 18

alright I got it now thanks for the help.

Answer 19

welcome To Openstudy !