# Vertical asymptotes, intervals of increase and decrease, local maxima and minima, concavity, inflection for $f(x)=1+(7/x)-(5/x^2)$

$$f(x) = 1 + \frac {7}{x} - \frac {5}{x^2}$$

(a) Find the vertical asymptotes.

I answered $1$ because if you plug in $0$ for $x$ you get $1$.

(b) Find the interval where the function is increasing.

I answered ($\frac {7}{10}, \infty$) because I got $f'(x) = \frac {1}{x}(\frac{-7}{x} + 10)$ and solved for x.

(c) Find the interval where the function is decreasing.

I answered ($-\infty, \frac {7}{10}$)

(d) Find the local minimum and maximum values.

I answered local maximum $=$ DNE and local minimum $\approx$ .7959.

(e) Find the interval where the function is concave up.

I answered ($-\infty, \frac{7}{5}$) because I found $f''(x) = \frac{1}{x^2}(\frac{14}{x} - 10)$. Then I solved for $x$.

(f) Find the interval where the function is concave down.

I answered ($\frac{7}{5}, \infty$)

(g) Find the inflection point.

I answered ($\frac{7}{5}, 3.45$)

According to WebAssign, I got all of these wrong. How come? Please help!

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You've asked three questions on this one pset in the past 3 hours. You haven't demonstrated that you've put a significant amount of effort in any of the questions. What's even the point of doing this homework if you are just going to get SE to do it for you? –  roliu Nov 11 '12 at 5:09
I listed everything that I answered. I have been working on this homework for the past few hours. I'm trying my hardest man calculous is really hard. And who are you to just come in here and reem me for asking three questions in the past 3 hours. Get out. –  dsta Nov 11 '12 at 5:12
Well, first of all roliu is one of the people you are asking help from, so being polite doesn't harm. Second the point of math.se is to help you understand and not solve your assignments. Third the derivative you computed is wrong and you should learn to derivate correctly before anything else. –  tst Nov 11 '12 at 5:32

## 1 Answer

For (a), if you plug in $x=0$, you don't get $1$ --- you don't get anything, since you can't plug in $x=0$, since division by zero is undefined. In fact, it's for that reason that $x=0$ is the vertical asymptote.

As @tst notes in the comments, your differentiation in (b) is wrong, and this undoubtedly messes up the answers for all the other parts.

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