Expert: Paul Klarreich - 11/28/2009

Question
can you show me the steps to take to address each on of the questions?  Thank you very much!
In each of the following problems, graph the function. Your answer should take
into account the following information:
(i) The domain of the function. (If not specified, assume the domain is the largest
possible on which the function makes sense.)
(ii) Horizontal and vertical asymptotes, if any.
(iii) Regions on which the function is increasing and on which the function is decreasing.
(iv) Local and global maxima and minima, if any.
(v) concavity and inflection points.

f(x) = (2 − x)e^x

Answer
Questioner: mikel
Country: United States
Category: Calculus
Private: No
Subject: Calculus
Question: can you show me the steps to take to address each on of the questions?  Thank you very much!
In each of the following problems, graph the function. Your answer should take
into account the following information:
(i) The domain of the function. (If not specified, assume the domain is the largest
possible on which the function makes sense.)
(ii) Horizontal and vertical asymptotes, if any.
(iii) Regions on which the function is increasing and on which the function is decreasing.
(iv) Local and global maxima and minima, if any.
(v) concavity and inflection points.

f(x) = (2 − x)e^x
...........................................
(i) See if there are any points where f(x) is undefined.(zero denominators, sqrt(negatives), etc)
(ii) find limit[as x -> +- infinity] if possible.
(iii) Find  f'(x) [need product rule] and set it = 0, to find your critical points.  remember that e^x is never zero or negative.  I think you'll get x = 1
(iv) Use part (iii)
(v) Find f''(x) and set.... to find inflection points.
I think you'll get x = 0.

Put it all together.  Yes, it is a lot of work.  I'm sorry if you expected me to do it all for you.