Max Extrema and Point of Inflection

[kari82]

1. find the extremas and points of inflections



2. g(t)= 1+(2+t)e^(-t)



3. So i know you need to find g(t)' and g(t)''

g(t)'= -e^(-t)(1+t)
g(t)''= (t)e^(-t)

my critical point is t=-1 (max) and my point of inflection is t=o

How do I get to max extrema being (-1, 1+e) and point of inflection (0,3)? Thank you very much!

 

[snipez90]

You've only given the x-coordinates of your critical point and point of inflection. The actual point is (t, g(t)). In other words you need to plug the values for t you have into the original function to get the corresponding y-coordinate.

 

[kari82]

Thank you so much! I knew it wasnt hard... I just couldn't figure it out. Thanks again!