# Thread: Study question about Curve Sketching.

1. ## Study question about Curve Sketching.

Ok so I have a test on curve sketching coming up, and I can't seem to get around how to do this question.

It says

Sketch the curve for the function y= (x^2+11x-22) / x^2
Include intercepts, extreme values, points of inflections and any other significant details.

When I start taking the derivative and expanding, I get some funky answers, its hard to see what im doing wrong.

2. Originally Posted by Skor
Ok so I have a test on curve sketching coming up, and I can't seem to get around how to do this question.

It says

Sketch the curve for the function y= (x^2+11x-22) / x^2
Include intercepts, extreme values, points of inflections and any other significant details.

When I start taking the derivative and expanding, I get some funky answers, its hard to see what im doing wrong.
Let me give you a hint that will help you a lot.

$\displaystyle \frac{x^2+11x-22}{x^2}=\frac{x^2}{x^2}+\frac{11x}{x^2}-\frac{22}{x^2}=1+\frac{11}{x}-\frac{22}{x^2}=1+11x^{-1}-22x^{-2}$
Thus, now taking the derivative is incredible simple.

3. You know, I know all about that, but I never figured about using it, thanks.

4. Originally Posted by Skor
You know, I know all about that, but I never figured about using it, thanks.
Thus,
$\displaystyle y'=-11x^{-2}+44x^{-3}=0$
Multiply by through,
$\displaystyle x^3$,
$\displaystyle -11x+44=0$
$\displaystyle x=4$.
Thus, the derivative is zero at four.