# Slope of curve

1. Mar 28, 2012

### rafay233

1. The problem statement, all variables and given/known data
Question: Find the slope of the curve at the indicated point.

y= (1/x-1) at x=2

2. Relevant equations
Don't know what relevant questions mean.

3. The attempt at a solution
(y(x+h) - y(x))/(x+h)-h
( (1/x-1 + h) - (1/x-1) )/h
( (1/2-1 + h) - (1/2-1) )/h
( (1+h) - (1) )/h
h/h=1

the problem is the book says it should be -1.
Help anyone?

2. Mar 28, 2012

### scurty

You need to be careful when writing math online. What you wrote as y= (1/x-1) implies $y = \frac{1}{x} - 1$. I suspect you meant to write $y = \frac{1}{x-1}$ as that function gives the correct answer.

You plugged in values wrong right from the start which is why your answer is wrong. Let's rewrite your function as $f(x) = \frac{1}{x-1}$. Now you need to compute $\displaystyle\lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}$. Now, what does $f(x+h)$ equal? Remember, you need to plug in the value (x+h) where ever you see an x.

3. Mar 28, 2012

### mtayab1994

I made a mistake on the tex look at the next reply.

4. Mar 28, 2012

### mtayab1994

Well this question is fairly simple, all you have to do is take the derivative of the equation:

$$f(x)=\frac{1}{x-1}$$ and then calculate the limit:

$$\lim_{x\rightarrow2}f'(x)$$ and you should get the same answer that your textbook has.

Ps: the derivative is the slope of the tangent line at a certain point.

5. Mar 28, 2012

### rafay233

could you guys tell me what you are using to make the fractions look like that? So no one gets confused?

6. Mar 28, 2012

### scurty

We are using a code called LaTeX, it makes all the math look pretty and readable.

I can give a quick little tutorial for fractions but to learn everything I'll redirect you to a website.

So, first of all, you must use TAGS to show that you want to type in code. The tags are
Code (Text):

. Everything between the tags will be put into code. What's nice about this forum is that if you see a pretty looking formula that was coded in LaTeX, you can right click on it and select Show Math As -> TeX commands to see what the code is. Try it out for ours above.

For basic fractions the code is
Code (Text):
$\frac{a}{b}$
which will look like: $\frac{a}{b}$. Everything you put in the first set of brackets will go in the numerator, everything in the second will go in the denominator. You can even do fractions in fractions:
Code (Text):
$\frac{\frac{c}{d}}{b}$
= $\frac{\frac{c}{d}}{b}$.