- #1

Vitani11

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## Homework Statement

Analyze the function f(x) = [(x

^{2}-7x+12)/(x-1)]e

^{-x/2}. Identify the zeroes, local maxima, and minima (approximate locations), as well as points where the function "blows up", give asymptotic values (for x→±∞), and sketch the function.

## Homework Equations

f(x) = [(x

^{2}-7x+12)/(x-1)]e

^{-x/2}

f'(x) = (e

^{-x/2}(12-7x+x

^{2})+(-1+x)[e

^{-x/2}(-7+2x)-((e

^{-x/2})/2)(12-7x+x

^{2})))

## The Attempt at a Solution

Above is the derivative. I can't just solve this thing for x, can I? It's hellish and involves logs and there is a high chance that I'll mess up. However the professor said approximate. So how do I do that? I was never formally taught how to approximate a functions local max or min. Do I binomial expand each term in the derivative after simplification of it and then find the zeros?

What about the asymptotes? Can't just do long division to find it because there is an e

^{-x/2}in there...

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