Question: What is the slope of the curve y= (1/x-1) at x=2?

[rafay233]

Homework Statement

Question: Find the slope of the curve at the indicated point.

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

Homework Equations

Don't know what relevant questions mean.

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?

 

[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.

 

[mtayab1994]

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

 

[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.

 

[rafay233]

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

 

[scurty]

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

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

[itex][/itex]

. 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

[itex]\frac{a}{b}[/itex]

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:

[itex]\frac{\frac{c}{d}}{b}[/itex]

= $\frac{\frac{c}{d}}{b}$.

To learn more if you want, try these two sites out:

http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Symbols
http://detexify.kirelabs.org/classify.html

 

[rafay233]

k thnks and btw i got the answere :D