1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Slope of curve

  1. Mar 28, 2012 #1
    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

    the problem is the book says it should be -1.
    Help anyone?
  2. jcsd
  3. Mar 28, 2012 #2
    You need to be careful when writing math online. What you wrote as y= (1/x-1) implies [itex]y = \frac{1}{x} - 1[/itex]. I suspect you meant to write [itex]y = \frac{1}{x-1}[/itex] 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 [itex]f(x) = \frac{1}{x-1}[/itex]. Now you need to compute [itex]\displaystyle\lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}[/itex]. Now, what does [itex]f(x+h)[/itex] equal? Remember, you need to plug in the value (x+h) where ever you see an x.
  4. Mar 28, 2012 #3
    I made a mistake on the tex look at the next reply.
  5. Mar 28, 2012 #4
    Well this question is fairly simple, all you have to do is take the derivative of the equation:

    [tex]f(x)=\frac{1}{x-1}[/tex] and then calculate the limit:

    [tex]\lim_{x\rightarrow2}f'(x)[/tex] 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.
  6. Mar 28, 2012 #5
    could you guys tell me what you are using to make the fractions look like that? So no one gets confused?
  7. Mar 28, 2012 #6
    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):
    which will look like: [itex]\frac{a}{b}[/itex]. 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):
    = [itex]\frac{\frac{c}{d}}{b}[/itex].

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

    http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Symbols [Broken]
    Last edited by a moderator: May 5, 2017
  8. Mar 29, 2012 #7
    k thnks and btw i got the answere :D
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook