The problem is differentiate x^2+1/x
Find the following:
1.)Intercepts

2.)Asymptotes
3.)Symmetry
4.)Domain
5.)Increasing/decreasing behavior
6.)Relative extrema
7.)Concavity
8.)Inflection Points

What i have so far
no intercepts
V.A(vertical asymptote) at x=0
H.A none
S.A y=x
symmetry at origin
increasing (-infinity,-1)
relative max (-1,-2)
relative min (1,2)

2. Look at its graph and see if you did it right.

3. Originally Posted by Tskate
The problem is differentiate x^2+1/x
Find the following:
1.)Intercepts

2.)Asymptotes
3.)Symmetry
4.)Domain
5.)Increasing/decreasing behavior
6.)Relative extrema
7.)Concavity
8.)Inflection Points

What i have so far
no intercepts
V.A(vertical asymptote) at x=0
H.A none
S.A y=x
symmetry at origin
increasing (-infinity,-1)
relative max (-1,-2)
relative min (1,2)
In the future you might try a larger font. This is difficult to read.

-Dan

4. Hello, Tskate!

$y \:=\:\frac{x^2+1}{x}$ . ← Is this what you meant?

Find the following:
1) Intercepts
$x$-intercepts: let $y = 0$
. . $\frac{x^2+1}{x} \:=\:0\quad\Rightarrow\quad x^2+1\:=\:0\quad\Rightarrow\quad x^2 \:=\:-1$ . . . no x-intercepts

$y$-intercepts: let $x = 0$
. . But $\frac{0^2+1}{0}$ is undefined . . . no y-intercept

2) Asymptotes
Vertical asymptote: . $y \,=\,0$ (y-axis)

Horizontal asymptote: . None

Slant asymptote: . $\lim_{x\to\infty}\frac{x^2+1}{x} \:=\:x\quad\Rightarrow\quad y \:=\:x$

3) Symmetry
Symmetry to origin (only).

4) Domain
All real $x \neq 0$

5) Increasing/decreasing behavior
$y' \:=\:\frac{x\cdot2x - (x^2+1)\cdot1}{x^2} \:=\:\frac{x^2-1}{x^2}$

Increasing: . $x^2-1\:>\:0\quad\Rightarrow\quad x^2\:>\:1\quad\Rightarrow\quad|x| > 1\quad\Rightarrow\quad(-\infty,\,-1) \cup (1,\infty)$

Decreasing: . $|x| < 1,\;x \neq 0\quad\Rightarrow\quad (-1,0) \cup (0,1)$

6) Relative extrema
Solve $y' = 0\!:\;\;\frac{x^2-1}{x^2}\:=\:0\quad\Rightarrow\quad x \:=\:\pm1\quad\Rightarrow\quad y \:=\:\pm2$

Second derivative: . $y'' \:=\:\frac{x^2\cdot2x - (x^2-1)\cdot2x}{x^4} \;=\;\frac{2}{x^3}$

At $x = 1\!:\;y'' = +2$ concave up . . . minimum at (1,2)

At $x = -1\!:\;y'' = -2$ concave down . . . maximum at (-1,-2)

7) Concavity
Concave up where $y'' > 0\!:\;\frac{2}{x^3} > 0 \quad\Rightarrow\quad x > 0$

Concave down where $y'' < 0\!:\;\;\frac{2}{x^3} < 0 \quad\Rightarrow\quad x < 0$

8) Inflection Points

Inflection point occur where $y'' = 0$

. . But: . $\frac{2}{x^3} \:=\:0$ has no solutions . . . There are no inflection points.

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