Consider the function #f(x)=e^(-x^(2))#?
Find the following:
- domain; found:
#(-\infty,\infty)#
- x-intercepts; found:
#-x^2=-\infty# thus there is NO x-intercept
- y-intercept; found:
#y=1#
- symmetry
- vertical asymptotes; found: NONE
- horizontal asymptotes; found:
#x=0# (exponential function rule?)
- intervals of increase and decrease
- local maxima and minima
- intervals of concavity
- inflection points
If any characteristics are not present in the function, state "NONE". Then graph the function
I apologize for the confusion regarding the parts I can understand/answer! I have worked out which ones I actually need help with now.
Find the following:
- domain; found:
#(-\infty,\infty)# - x-intercepts; found:
#-x^2=-\infty# thus there is NO x-intercept - y-intercept; found:
#y=1# - symmetry
- vertical asymptotes; found: NONE
- horizontal asymptotes; found:
#x=0# (exponential function rule?) - intervals of increase and decrease
- local maxima and minima
- intervals of concavity
- inflection points
If any characteristics are not present in the function, state "NONE". Then graph the function
I apologize for the confusion regarding the parts I can understand/answer! I have worked out which ones I actually need help with now.
1 Answer
See below.
Explanation:
Symmetry
So the function is even and the graph of the function is symmetric with respect to the
Increase/Decrease and Extrema
Since
So
Concavity and Inflection
# = 2e^(-x^2)(2x^2-1)#
Analysis of the sign of
on
on
on
Therefore, there are two inflection points:
(Note that