(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use the function y=2e^-0.5x^2 to answer the following questions

a) state the domain

b) Determine the intercepts, if any

c) Discuss the symmetry of the graph

d) Find any asymptotes

e)determine the intervals of increase and decrease

f)what is the maxima and/or minima

g) where is the curve concave upwards and downwards?

h) locate the points of inflection

2. Relevant equations

3. The attempt at a solution

im having the most difficult with understanding this function since i have never worked with anything like this but this is what i have so far, i would appreciate help me with the steps i have done wrong or dont know how to complete

a) state the domain

-22<x<22

b) Determine the intercepts, if any

y-intercept: y=2 the point is (0.2)

x-intercept: there are no x-intercepts

c) Discuss the symmetry of the graph

the graph is symmetric with respect to the y-axis, as the original equation is unchanged when x is replaced by -x

d) Find any asymptotes

vertical asymptotes: as x approaches -22, e^x decreases to 0; and as x approaches 22 e^x decreases to 0. Therefore the y-axis is a vertical asymptote.

vertical asymptotes: there are no vertical asymptotes as the graph never crosses the x axis

e)determine the intervals of increase and decrease

y=2e^-0.5x^2

dy/dx=2e^-0.5x^2 * d/dx (-0.5x^2)

dy/dx= -3xe^-0.5x^2

since the sign of the first derivative is the different then the sign of x

dy/dx<0 when x>0, and dy/dx<0 when x>0

( im pretty sure that ones wrong)

f)what is the maxima and/or minima

Max: (0,2)

Min: 0 (not sure about that)

g) where is the curve concave upwards and downwards?

dy/dx=-3xe^-0.5x^2

second derivative:

-3x d/dx(e^-0.5x^2) + e^-0.5x^2 d/dx (-3x)

-3x * e^-0.5x^2 * 2x + e^-0.5x^2 * -3

= -3e^-0.5x^2 (3x^2 +1)

the second derivative is negative meaning the graph is concave down

h) locate the points of inflection

there are no inflection points

(unsure about that aswell)

i know this is so long but i would really appreciate help on this problem i would like to learn how to do this right.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Describing the exponential function y=2e^-0.5x^2

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