Posted by **Catherine** on Wednesday, April 6, 2011 at 12:07am.

Please answer the following questions about the function

f(x)=e^(-0.5x^2)

Instructions: If you are asked to find x- or y-values, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use interval notation if you are asked to find an interval or union of intervals, and enter { } if the interval is empty.

(a) Find the critical numbers of f, where it is increasing and decreasing, and its local extrema.

Critical numbers x=

Increasing on the interval

Decreasing on the interval

Local maxima x=

Local minima x=

(b) Find where f is concave up, concave down, and has inflection points.

Concave up on the interval=

Concave down on the interval =

Inflection points x=

Find any horizontal and vertical asymptotes of f.

Horizontal asymptotes y=

Vertical asymptotes x=

My answers were:

Critical numbers x= none

Increasing on the interval = didnt have anything

Decreasing on the interval =(-INF,-0.5)U(-0.5,0.5)U(0.5,INF)

Local maxima x= none

Local minima x= none

Concave up on the interval= (-0.5,0)U(0.5,INF)

Concave down on the interval = (-INF,-0.5)U(0,0.5)

Inflection points x= none

Horizontal asymptotes y= none

Vertical asymptotes x=none

Amost none of them is right, only the local minima and the vertical asymtote, please help, I'm not sure how to do this problem.

- Calculus (urgent!!) -
**Mgraph**, Wednesday, April 6, 2011 at 10:13am
Critical number x=0

Increasing on interval (-Inf,0)

Decreasing on interval (0,Inf)

Local maxima x=0

Local minima x=none

Concave up on (-Inf,-1)U(1,Inf)

Concave down on (-1,1)

Inflection points x=-1,x=1

Horizontal asymptotes y=0

Vertical asymptotes x=none

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